Just had a bit of a look.
First, I think you need to knock down the “S” target, then land in the “S” hole to score the 5000 points and in that order.
I’m sure you know that to score 5000 pints, we pulse the 1000 points RE 5 times, scoring 1000 points each time.

(Part 1)
Looking at the schematic. The “S” hole RE will energise when you close the SW in “S” Hole. (Blue Line) The “S” Hole RE can start the SCR Motor, when the SCR Motor starts SW A1 will open but the “S” hole RE will stay energised vis its own hold Sw (Green line) until the SCR Motor reaches the end of its rotation, when SW E1 opens on the SCR Motor.
It sounds like this bit is working from the OP.

When the “S” Hole RE is energised, if you had already knocked down the “S” target, you should score 5000 Points.

(Part 2)
When you knock down the “S” Target, the make/brake SW for this target will change state from how it is drawn on the schematic, making a path to the 1000 RE. When the ball lands in the “S” hole, the “S” Hole RE energises closing another SW in the same circuit and stating the SCR Motor, SW C6 Located on Cam 2 of the SCR motor will then pulse the 1000Point RE 5 time. (Red Line)

Looks like you only have four SWs to check, and/or maybe a jones plug.

help-571.jpg

Ok it takes multiple hits of the ball return kicker and the ball never makes it out of the hole re-landing in the outhole switch but eventually kicks out but not after counting up the ball count.
You either have a playfield switch adding points and allowing the index re. to lock in or a ball index relay contact is close and shutting thus allowing it to lock in to allow the ball count to step-up to complete circuit.
If you are getting points when this happens then you have a playfield switch thats the culprit if not then a ball index contact is close.
Clean your outhole switch and the ball return re. contacts to get good strong continuity for a strong kick to that kicker coil.
▬▬▬▬Related contacts [snips] to clean/adjust ▬▬▬▬

1=Hollywood ball index.JPG
2=Hollywood ball index relay.JPG
3=Hollywood ball return.JPG
4=Hollywood impulse cam.JPG

These guy's are both spot-on with their replies. Also clean the plunger and change the coil sleeve for the ball kicker. I wouldn't be surprised if you found an aluminum sleeve in that coil...not a good thing.

That too. ↑
One other thing i might add is a slim chance of worn area on the wood at the playfield outhole that may be similar to a Gottlieb that can wear and not let the ball get a good strike and interfere with sending the ball on the first shot.
Easy fix if that happens.

On that age of game, those sleeves are normal. As you re-build the items - pops, slings, flippers, etc, just replace them with new nylon ones.
Congrats on the repair, glad you figured it out.