Hi pbd
there are two opinions / concepts:
AAA) First do a full cleaning and the cosmetically part - means cleaning every switch on every relay - take apart every unit to clean and adjust. Second look for faults / faulty behaving and do fix the nonworking parts.
BBB) First bring the pin back to working condition / fully running (might have to clean a switch here and there). Second do the cosmetic work - make it shiny.

I am a BBB-type of EM-Lover - main argument / reason / criterion: IF (if) I cannot bring it back to life then I would have wasted time on cleaning / cosmetics.
I have no problem when a AAA-type of EM-Lover does it his way.

You mention "Scoring issue points switching between players - maybe a fault in the Scoring Reels".
I do not know if this means "when playing a ball - sometimes (simply playing) the next points are added on the second or maybe third or fourth player".
OR: Does it means "a single-player-game has started - but after (player-1) ball-1 the pin faulty changes to player-2-ball-1".
Either way: The Score-Reels are "Slaves" they obey and work what a "Master" orders - so we have to look for the fault in the interaction of relays / steppers / (Score-Motor).
Of course, a Score-Reel might not step because of sticky old grease or other mechanical reasons - or a coil is shot.

So a good description of the fault(s) would be very helpful. Greetings Rolf

I had a Hang Glider a couple years ago that when I first started it up the over-the-top buzzer was stuck on...scared the shit out of me! I didn't know what it was...pretty cool feature though. It's a fun game but the guy in the speedo is creepy...

Hi pbd
great, ipdb http://www.ipdb.org/machine.cgi?id=1112 has the schema and the manual, -> manual-page-12: Which Units / Relays are mounted in the bottom of cabinet. So the rest are mounted on the underneath-side of the playfield or in the backbox.

The ball on the playfield makes (lets say) 10 points - means the 10-point-RELAY is activated -> which player shall get the 10 points on HIS Score-Reel ? This is handled by the Player-Unit - it routes the signal from the pulling 10-point-RELAY to the appropriate player. I think here: http://www.ipdb.org/showpic.pl?id=1112&picno=46384 -> on the right is the Player-Unit.

Whenever You just "look at / work / clean": UNPLUG the main power cord (Safety Reasons, Danger: 110 VAC and 50VAC and 6VAC around).
The Player-Unit (as Coin-Unit and Ball-Count-Unit) is a "Total-Reset-Stepper" - it has two coils mounted. Imitate "coil gets current and pulls" -> by hand move the plunger of one coil.
One coil does step-up single steps (-> up -> up -> up) - the other does "open mechanical switches" -> wroamm / bang -> the unit steps all the way down (the spring sitting on /around the axis does the job).
Try stepping up / stepping down (by hand) this unit - easy going ? securely stepping ? do the wiper-fingers sit on the middle of the rivets ?

We had a similar problem - well in a WILLIAMS -> https://pinside.com/pinball/forum/topic/space-mission-mostly-works-but-nothing-is-scoring -> post-14 -> JPG -> encircled "yellow-brown" -> the Player-Unit routes the signal (in post-27 the "involved Switch on Tilt-Relay" is also shown).

I belive the BALLY-Player-Unit is built a bit different - no snoe-shoe wipers but wiper-fingers (?).
The (ipdb) schema has information about the Wire-COLORS -> schema-C-4 / C-5 shows a "wire-25-7" connecting the "Switch on 10-point-relay" to the Player-Unit. And a "wire-18-2" routes the current to the Score-Reel-player-1 (wire-23-7 to ...-player-2).
The schema shows (at B-50) the color-code: 25=blue-white, 18=red-black, 23=blue-yellow.
Look at the Player-Unit -> see wire-25-blue-white solderd-on on a lug -> some connection through wipers -> wire-18-red-black.

Plug-in the main powr cord, start a two-player-game -> play the balls -> check now and then the Player-Unit -> do the wiper-fingers sit neatly in the middle of the rivets ?

Well, it might be: insulation of wires are old, falling of at some places -> now and then a "short" does happen (?).

If You want to go the "AAA-type way" -> http://user.xmission.com/~daina/tips/pub/emTips.html -> http://user.xmission.com/~daina/tips/pub/tip0096.html .
Greetings Rolf