I don't have a Fantasy schematic but this is from the New World schematic on IPDB.org which may be similar:
New World player relays (resized).jpg
After starting a game if you then press the Replay button again the P relay should fire and the Score Motor should run and the J2 relay shown above should fire for player 2. Pressing the Replay button again should fire J3 for player 3 and the final Replay button press should fire J4 for player 4.

Check if the P relay fires and whether the switch in red above closes.

/Mark

The first thing to check is whether the Balls Played step unit operates properly. With the game unplugged you should be able to push in the plunger on either solenoid and release it and have the step unit cleanly step up or back to the next position. This should work well in all 21 positions. If not you should clean it until it can step reliably when you activate it manually.

Once the Balls Played unit steps reliably when manually activated we can look for an electrical issue.

Here is a portion of the New World schematic. Fantasy may not be the same.
New World ball count (resized).jpg
The bottom portion of the schematic shows that the Balls Played unit has 21 positions. It also shows that each position fires one of the T1-T4 relays to determine which player is currently playing and accumulating points. Can all four players in your game score points, or just player 1? Does the Balls Played Unit advance when the ball drains?

The number of times the Balls Played unit advances when the ball drains is determined by the number of players. The top part of the schematic shows that when the ball drains the Ball Played unit can step 1-4 times. The Motor IMP A switch in the upper right corner generates 5 pulses when the Score Motor turns. One pulse always gets through the Motor 2B switch to advance the Balls Played unit one step to the next position. The other three paths (through switches on J2, J3 and J4) allow more pulses to get through and advance the Balls Played unit if appropriate. So for example on a 2 player game, the Balls Played unit should step just once (through the Motor 2B switch) when player 1 drains, but it should step 3 times (through the Motor 2B, J3 and J4 switches) when player 2 drains to return the Balls Played unit to a position where the T1 relay fires and player 1 is scoring.

See if you can determine when it works and when it doesn't. Does it work properly on a 1 player game? On a 2 player game? etc... When does it take the correct number of steps after a ball drain and when does it take too many steps?

Try some experiments on a 5 ball game to see how that compares. Also listen for and count the number of steps the Balls Played unit takes each time the ball drains. When does it take extra steps? Or, does it take a single step that advances more than one position?

It's hard to say without a good copy of the correct schematic and a manual if there is one. If the online retailers don't have a copy there are several Fantasy owners listed on Pinside and on http://www.pinballowners.com. You might reach out to them to see if any can help with the game behavior or better yet a schematic.

Based on the New World schematic which is not clear in places, it seems that the through switch should fire the Y and Z relays which then allow the balls played unit to take the appropriate number of steps through the circuit shown above. The Y relay may wait for a bonus to count down first before firing and allowing the balls played to advance. Avoid a bonus for now if you can to simplify the troubleshooting.

At reset the balls played unit should return to the 1st (leftmost) position shown in the schematic in reply #4. When the ball is kicked to the shooter lane the trough switch should close to advance the balls played unit one step (to the right in the schematic) so that the T1 relay fires. Then it will be in player 1/ball 1 position (2nd from the left in the schematic).

To get much further you'd need to better characterize when the balls played unit takes the wrong number of steps and how many steps it takes when it's wrong.

The fact that the Trough switch works if you hold it down longer is a good clue to what may be happening. Here are some more sections of the New World schematic:
New World ball count 2 (resized).jpg
I think this is how it should work...

When the Trough switch (right side, in red) closes it should immediately fire the Z relay. When the Z relay fires it closes the Z relay switch next to the Trough switch and fires the Y relay (left side in red) too. Once the Y relay fires it should close its own Y relay (or lock in) switch so that the Y relay is held active through the Score Motor 6C switch path (in red) until the Score Motor 6C switch opens.

When the V relay fires it should also start the Score Motor turning (not shown). As the Score Motor turns the IMP A (Impulse cam) Score Motor switch (in red, upper right) closes 5 times to send 5 pulses towards the "add balls played" solenoid. One of the pulses from the IMP A switch goes through the the Motor 2B switch (in red) and through the Y relay switch (in red) and gets to the "add balls played" solenoid either through the Z relay switch or through the other switch on the balls unit (not sure which). More pulses might get to the "add balls played" solenoid if the game needs to skip over some players. In a one player game for example three more pulses should get to the "add balls played" solenoid to skip over players 2, 3 and 4. The extra pulses will go through the J2, J3 and J4 switches respectively.

After the balls played unit has taken the correct number of steps (and the Score Motor is still turning) the Score Motor 6C switch opens to relax the V relay. The Score Motor should stop shortly after that. In other words the V relay needs to stay on for most of the Score Motor's 180 degree turn while the game sorts out how many steps the balls played unit should take.

If your V relay is relaxing as soon as the Trough switch opens it will open up the V relay switch in the path to the balls played unit too early and prevent most or all of the required pulses from getting through to the "add balls played" solenoid.

You can test this by manually closing the V relay with a stick or other insulator. It should stay activated until the Score Motor has completed most of its 180 degree turn. If it doesn't either the V relay switch or the Motor 6C switch isn't closing properly.

The motor chart at the bottom shows you where to find all of the Score Motor switches. The motor itself is on the right and the black bars represent the 8 cams of the Score Motor in order. The Motor 6C switch for example is in the switch stack on the #6 (or leftmost) cam, third switch up from the bottom in the stack. The numbers inside the boxes in the motor chart are the schematic locations of the switches which aren't as interesting in this situation.

Please send a good scan of the schematic to IPDB.org if you can.

I don't know what you mean by "checked". Unless you've proven that they each conduct electricity when they should don't dismiss them.

Does the V relay behave as described in my last reply?

When the Balls Played unit takes the wrong number of steps does its advance solenoid fire once for each step taken (which would imply a circuit issue), or does the unit sometimes fail to step or step multiple steps each time the solenoid fires (which would imply a mechanical issue)?

If the Balls Played unit advance solenoid is firing the wrong number of times you need to trace through its circuit shown at the top of reply #14. Are the switches on the T and J relays working properly?

As the Balls Played unit steps through its various positions do the T1-T4 relays fire one at a time as shown in the circuit in reply #4? Each one represents the current player (T1 is player 1, T2 is player 2, etc.). Even if a player is being skipped its relay should fire briefly as the Balls Played unit steps over each position.

Do the J relays fire as you add more players (J2 - 2nd player playing, J3 3rd player playing, etc.)

If the ball trough switch is doing the right thing, perhaps the Ball Return solenoid isn't firing at the right time. Where is this solenoid on the schematic and what drives it?
Fantasy solenoid chart (resized).jpg
Also a good schematic scan would be much more helpful.

I'm curious why there are two trough switches in the schematic above (highlighted in blue marker). Are they in the same place in the game or is one in the out hole and the other in the trough to the shooter lane?

I any event when the ball drains the Y and Z relays should both fire. One of them probably starts the score motor turning.
Fantasy ball return (resized).jpg
Once the score motor is turning and the Y and Z relays are active the "add balls played" solenoid (in the red box) should fire when the Score Motor 2C switch (red box) closes. Soon after that the "balls return" solenoid (red box) should fire when the Motor 4C switch (red box) closes. It sounds like these might be happening out of order.

If your score motor has a service jack, or jones plug that can cut power to the score motor, you could try draining the ball and then manually turning the score motor slowly so see if these two things happen at the right time.

That's surprising. Other Playmatic games of that era have one. Could you just block the motor switch in the red box with a piece paper?
Fantasy motor (resized).jpg
You could also find the two switches in question, M2C and M4C, and turn the motor by hand with the power off to see when they close relative to each other.

Interesting. According to photos on IPDB Playmatic used both Gottlieb style (vertical shaft) motors like the one above and Bally/Williams style (horizontal shaft) motors, apparently changing over in 1976:

Gottlieb style motors:
1974 Joker
1974 Harem
January 1976 Fantasy

Bally/Williams style motors:
June 1976 Fiesta
October 1976 New World
May 1977 Speak Easy
June 1977 Rio

Your schematic may have a Score Motor diagram showing the positions of various switches. If not, the Gottleb chart at https://pinside.com/pinball/forum/topic/gottlieb-far-out-schematic-error#post-6159755 might help. The Gottlieb chart shows where the various switch stacks are around the motor, but it doesn't show where the switch is in the switch stack. You may need to rely on wire colors from the schematic to identify the specific switches.

When you disassembled the motor did any of the switch dogs (in the red box below) or anything else fall out? On Gottlieb motors the switch dogs can mount in two different positions and mounting it in the wrong position will definitely change the relative timing of the switch stacks. Playmatic apparently had not only two positions to mount the switch dogs, they had two switch dogs of different lengths doubling the possibilities.

Fantasy motor switch dog (resized).jpg

Do the "add balls played" and "ball return" solenoids fire when their score motor switches close? Or do they fire at some other time? Refer to the schematic in reply #26.

That's not right.

I hope that's a typo because earlier you said that 2C fires before 4C. Either way I think you've identified the problem. It sounds like the ball return fires before the motor 4C switch closes. Whether it also fires with the motor 2C or some other motor switch it sounds like you have a short that you'll need to find.

If you're lucky there's some kind of obvious short on the score motor switches like a bent solder tab, solder blob, bare wires touching, bent switch leaf, etc. If not you'll need to study the schematic to figure out where else wires from the motor 4C and 2C switches might cross paths. Are they both on the same stack of relay switches somewhere? Do they both go through a jones plug? Etc.