I have the add-a-ball Fun Park, but I'd have to think that part of the start up would
be the same. The 1's, 10s, and 100's score reels reset from a switch in SB1 (Start Relay).
The 1,000's reel resets from a set of switches in SB2 (Start Relay). Both Relays are in the
Control Bank. The 1s, 10's, and 100's pulsate from Score Motor 4A. The 1,000's from 1A.
Score Motor 1A is for other functions also, so I'm sure that's okay, but it looks like 4A
is only for the 1's, 10's, and 100's reset..

Actually, I do have a 1954 Team Shuffle, and went through many bowlers. I put many bowlers
out. Got really good with them. Rarely need schematics..
Yes, Fun Park is a single player also, but has two Start Relays. SB1 and SB2. They both fire
at the same time at start up.
The coin switch (or free play button) should energize the SB Relay. You'll want to check the
Anti-Cheat switch to make sure it's making good connection.
Edit: I think you mentioned the SB Relay didn't energize during game play, but it must at
start up, right?

If everything works except for the score reels not resetting, the SB Relay must be energizing at start
up or how would the score motor get energized and the ball count unit reset? The SB Relay should be
the first thing to energize once you hit the free play button and it doesn't energize during game play.
Only at start up. With the playfield open, if you look at the SB Relay when you hit the free play button,
I'm sure you'll see the SB does energize. I don't have Funland, so I'm not sure about it's exact start up
procedure, but maybe the problem is in the SB Relay, but I expect maybe it's a set of switches in the
Score Motor. First maybe you can confirm that the SB Relay is energizing at start up, then if you want,
you can take a pic of the "Add Ones Unit" "Add Tens Unit" "Add Hundreds Unit", and Add Thousands Unit"
from the schematics. Those Units represent the score reels. I believe you mentioned you had a schematic.
They're probably located toward the bottom portion of the schematic..

I just went through a Cowpoke, but it's start up is different than Fun Park.
I'm not sure about Funland, but for sure the SB Relay would be the very first
relay to energize from the free play button which resets the score reels and
ball count unit. On Fun Park, once the score reels are all reset to 0, and the
ball count has totally reset, the Reset Relay (also in the Control Bank) will
energize and then when the ball count steps up to the 4th position, a switch
is made from the ball count's plunger arm which energizes the big coil on the
Control Bank then the SB and Reset (known as DB on Fun Park) Relays are
reset. At start up is the only time the SB (Start Relay) energizes..
I guess it's possible all score reels run-out switches are not adjusted corrected
and/or dirty, but I would think the chances are more likely it's switches in the
SB Relay, but maybe even more likely a set of switches off the Score Motor's
cam. On Fun Park, it's Score Motor switch 4A, but maybe someone with a
Funland along with it's schematics will be able to help out. You mentioned that
score reels don't reset, but yet the Funland will go into game mode and be able
to be played. On the very few Replay Gottiebs I went through, I can't remember,
but on Fun Park (and other Gottieb add-a-balls), unless the score reels all zero
out, the Reset Relays circuitry will not be completed, and it won't go into game
mode. The score motor just remains energized letting the machine know that
all the score reels are not reset to 0..
Anyways, when you press the free play button (or drop a coin) and if the score
motor then runs, the SB relay has to be energizing, and if it then stops, the Control
Banks big coil must be energizing also resetting the SB Relay..