There's a schematic on ipdb.org that shows there's one thing that those lights all have in common...
Aladdin's Castle Ball in Play lights (resized).jpg
I'd start there.

/Mark

Is the spider keyed, or could you have put it back in the wrong position (rotated 180 degrees from where it should be for example)?

To take a step back for a moment, a little detective work should help narrow down where the problem is.
Aladdin's Castle Ball in Play lights 2 (resized).jpg
You said that all the other lights work so the General Illumination lights on the left side of the schematic probably work which means that power is getting from the brown wire at the bottom to the yellow wire at the top.

If the "One Can Play" and "Two Can Play" lights work (one at a time) that's more evidence that the brown wire is good.

At the end of the game, does the Game Over light work (right side of the schematic)? If so we know that the Normally Open part of the Make/Break switch on the Game Over relay can get power from the brown wire to the blue-yellow wire.

That just leaves the Normally Closed part of the Make/Break switch on the Game Over relay, and the grey-white wire to the Ball Count unit as the likely problem.

As MrBally suggested the problem could be at the switch or anywhere between the Game Over relay and the Ball Count unit.

If you want to learn more about your game there's also a pretty good manual on ipdb.org. Read it through few times because you'll pick up something new each time.

The Game Over relay is an interlock relay with two coils. The armature can mechanically lock into either the Latched or Tripped positions and stay there indefinitely. The Latch and Trip coils move the armature from one position to the other when they fire momentarily. An interlock relay is used to remember something without using power. The Game Over relay will latch at the start of a new game and stay there until the end of the game when it will trip. It sounds like your Game Over Trip relay is firing early. (You should check the position of the Game Over relay during and after a game, and after you see the problem to confirm that that is what is happening.)
Aladdin's Castle Game Over relay (resized).jpg
There are three situations that can fire the Game Over Trip relay as shown on the schematic above.

1) The Lock relay switch (which should be open during a game) can close
2) The Ball Count Unit Zero switch and the Coin relay switch can close together
3) The Ball Count Unit disc can step up to position 6 (in a 5 ball game)

It could be that your Lock relay switch is closing early for some reason, or that the Ball Count Unit is reaching position 6 early. The Coin relay path is less likely but still possible. Check that the Ball Count unit wiper disc lines up exactly on the contact rivets below in every position. You can also slip folded pieces of paper between the contacts from the Lock relay and Coin relay switches to disable those paths. If the problem goes away, remove the paper one switch at a time to figure out which of the three paths is the culprit.

Can you get the same result if you gently pound on the playfield near the rollover lane during a game? It could be that the rollover switch is gapped too close and the vibration of the pop bumper is momentarily closing it.

The Start or Credit Button is shown at about 12D on the schematic. It should fire the Credit relay directly above it on the schematic. If that's not happening you'll need to check the switches in the Credit relay circuit.

A few things to check:
- Are there credits on the game?
- There's a switch in that circuit controlled by the Game Over relay which is an interlock relay. Does manually flipping the Game Over relay to the other position make the Credit button work?
- Does it work if the Ball Count unit isn't at zero?

That sounds like a weak connection in the Ball Count unit itself. If you look at the schematic in reply #2 the grey-white wire gets into the Ball Count unit somehow and out to the two wiper fingers for the ball in play and player up lights. Since neither set of lights work it's less likely that those wipers are the problem and more likely that it's a problem with the way the grey-white wire is conducted through the unit. Without seeing the layout of the stepper it's hard to say how that's done. It could be that there's a third wiper finger that picks up the grey-white wire through a set of ten consecutive contacts wired together. If that wiper doesn't have enough tension or somehow isn't making good contact with the contact board that could explain the lights being out. It could also be something like a bad solder joint on the grey-white wire solder lug on the Ball Count unit.

Try starting a game and then gently pressing the ends of the wiper fingers on the Ball Count stepper one at a time onto their contacts to see if they're making good connections. If you're lucky you might find a wiper that when pressed turns those lights on. You can use something like the eraser end of a pencil to gently push on the wiper fingers if you're not comfortable poking around in a live game.

BTW, when you "manually forwarded the Spider" you did that by pushing in the solenoid plunger or grabbing the toothed gear and not by grabbing the wiper fingers, right?

The lights operate at 6.3 volts AC while the coil operates at 50 volts AC. I believe the wire leading into the coil is a faded white-black wire to the step up coil, but you'd need to check that against the schematic to be sure.

I think the wires you're looking for to control the Ball in Play lights are the the ones I've pointed out here:
Aladdin's Castle Ball in Play lights 3 (resized).jpg
A few of them are hard to make out from the photo but the layout seems consistent. If you look at the schematic you'll see that each Ball in Play light is tied to two consecutive contacts on the board. Each time the ball drains the Ball Count unit takes one step in a two player game, or two steps in a one player game, but the Ball in Play light only advances on every other step.

If you probe around with your multimeter (and the power off) I think you'll find that each of the five Ball in Play light wires shown are tied to two consecutive contacts on the contact board. One of the wiper fingers will touch each of those ten total contacts one at a time as the unit steps through all the balls in play. How that wiper is connected to the grey-white wire is unclear from the photo, but it could be the wiper that's fixed to the contact board and makes contact to the underside of the wiper arm assembly:
Aladdin's Castle Ball in Play lights 4 (resized).jpg
There could be a bad connection between that wiper and the rest of the wiper arm assembly.

Have you checked the the paths with a meter, or just visually checked that they look good? Unless you have already, I'd recommend testing with a multi meter:Aladdin's Castle Ball in Play lights 5 (resized).jpg
- Unplug your game.
- Set your meter to its lowest resistance setting.
- Clip one test lead to the brown wire (1) and leave it there.
- Clip the other test lead to the brown wire too (1) and verify that the resistance is less than an ohm. That's about the value you'll want to see at all of the remaining test points.
- Move the 2nd lead from the brown wire (1) to the solder lug on the make/break switch on the Game Over relay with the grey-white wire.
- Manually toggle the Game Over relay from one position to the other and observe there resistance reading in the two positions. One position should measure less than an ohm, the other position should measure something much higher. Leave the Game Over relay in the position that measures less than an ohm.
- Move the lead from the Game Over relay solder lug to the grey-white wire wherever it attaches to the Ball Count Unit (3). You should still measure less than an ohm.
- Move the lead from the grey-white wire to the solder lug on the Ball Count Unit with the brown-red wire shown in the photo (4)
- Put the Ball Count Unit in position for ball 1. You should still measure less than an ohm.

At any of the four points if you're not measuring less than an ohm the problem is between your meter probes.

If you don't know what position the Ball Count Unit should be in for ball 1, step the unit through all of its positions to see which one gives you a measurement of less than an ohm.

When the Game Over relay and the Ball Count unit are in the correct positions there should be a near dead short path (about an ohm or less) between the brown wire on one end and the brown-red wire on the other end. If you're not measuring that, that would explain why your lights are not working.

You should be able to pick any two positions in the annotated schematic (1, 2, 3, or 4) and measure about the same very low resistance between those two points. If not, your problem is in the circuit between the probes. So if you can't measure a low resistance through the Game Over relay switch for example, figure out why. That may be the root of your problem.