Okay, the pin lights are lit so the Yellow Common is feeding the Pin Deck..
The Pin Reset motor doesn't energize to reset the pins. From what I gathered,
it sounds like they don't, but to confirm, if you manually reset the pins, then
activate the rollovers, the relays in the Relay Bank energize, and do the pins
go up?

Seems the Yellow Common wire is alive to the pin deck if the pin deck lights
are lit, but you might want to check (recheck) the Pin Deck's plugin (Jones Plug)
on the right inner wall near the rear maybe a couple feet from the Ball Lift box.
That feeds the pin's circuit coming from the Bank Relay..

If all looks good there, on the pin deck, the Yellow Common wire is connected to the metal of
one of the pin units, then the rest of the pin units are tide together with small flat stock.
Make sure that Yellow Common wire is making good connection to that one pin unit..

Yes. My mistake, Black is the common for the Pin Units. Yellow
for the Pin Lights.
The Pin Reset Motor and Pin Reset Relay (also on the Pin Deck)
has the Black for the common, so it appears the Black isn't feeding
to the Pin Deck. Did you check the Pin Deck's plugin which is on the
inside wall (the wall the hinges are on and just left of the big coffin's spring?
Check the Black wire on both the male and female of the plugins.
Because it's not feeding the Pin Units or Pin Reset Relay, it seems there's
probably some sort of bad connection and not making it up the Pin Decks
pig tail. Another thought is with the coffin is open, check where that Pig
Tail bends back and forth (rear of the machine, left hand side) when the
coffin is opened and closed. Might be a bad spot in the wire..

You have one of the few Bowling Alleys with the Ball Gate still attached.
Back when, they gave the Vendors so many problems, they just detached them..
Yes, the Black wire off the Coin Relay would be a good place to jump from, and
if still no luck, bypass the plugins and go right to the black on the Pin Deck.

And the pins also reset if you manually press the Pin Reset Relay (the relay on the
Pin Deck next to the Pin Reset motor) right?
The Pin Reset Relay energizes through the Score Motor's Wiper Board. If you hadn't
already, I'd first take off the wiper and clean then lightly lube the Wiper Board and also
inspect the Wiper's rivets.
Maybe you want to keep everything original, but if you continue to have problems
with the Ball Gate, I'd maybe take off the piece that keeps the balls from rolling..

The Score Motor's wiper's resting position looks okay.
So when you manually activate the Pin Reset Relay, the
Pin Reset Motor does energize.
While playing the machine, when the pins are suppose to
reset, the Pin Reset Relay doesn't energize?
When touching the (run-out) switches together on the Pin
Reset motor, the Pin Reset Relay shouldn't energize. The Pin
Reset Relay is what first energizes the Pin Reset motor, then
the Pin Reset Motor's run-out switch takes over..
On the #1 Pin not going up. Make sure the set of contacts on the
#1 Pin Unit is closed and making good contact when the pin
is down (in the reset position). There's also a set of contacts
in the #1 Relay (in the Relay Bank) that makes and energizes the
#1 Pin when #1 Relay is in the energized position..
It's strange that the #3 Pin wire shorted. I'm sure it was, but
when jumping, the wire was for sure on the proper terminal?
Does the #3 Pin coil look burnt?

Okay, if you look around the area where the Pin,s Jones Plug is (the
Jones plug you've been working on) there's 2 sets of switches that open
when the coffin (playfield cover) is opened, and those 2 sets closes
when the coffin is closed. One set closes the circuit to the Ball Lift
Motor (can't remember which set, but maybe has thicker wires because
the Ball Lift Motor is 110V), and the other set closes the circuit to the
Pin Relay. You'll what to make sure those switches are clean and closing
when the coffin is close. You can elegator clip them for testing.
United felt it was best for both the Pin Reset Relay and the Ball Lift
Motor didn't energize when the coffin was open, which certainly makes sense.
The 2 wires on the set of switches that go to the Pin Reset Relay are
Gray-Red and Gray-White. The Gray-White should be the one in the Pin
Deck,s Pig Tail. So if those switches are clean and making connection and
the Pin Reset Relay still doesn't energize during game play, you can jump
from those set of switches to the Gray-White on the Pin Reset Relay's coil
and if it works, then you'll know it's another bad wire (Gray-White)in the Pin
Deck's Pig Tail..
The good size rubber piece should be attached in the Ball Lift box and that's
what the ball first hits after rolling under the pins and leaving the alley. It
absorbs the punishment it would give hitting the Ball Lift Box's back door.
You'll see 5 holes where it bolts to with what I consider as very thin bolts,
thus I've found some of those bolts broken on some Bowling Alleys.
What I do is drill and make those holes 3/16", line up that rubber backstop,
(that thin rubber faces the front of the machine so that's what the ball would
hit first), then with a Phillip screw bit in a drill, fasten the backstop with 3" deck
screws. I have 3 or 4 Bowling Alleys out on location, but none set up here,
however I may be able to sneak a camera in a ball lift box from one in the barn
and take a pic of the rubber's backing to show exactly where it's mounted..
It's pretty important that it's remounted where it should be..

Yea, and maybe jump right off the Gray-White set of switches that the Coffin cover closes.
I checked, and without much work, I couldn't get to the back side of a United Ball Lift box,
but if you have and questions, I can take a pic from one of the ones uptown..

It sounds like the pins are finishing its reset before the Bank Relay
resets which would mean the Score Motor is running too slow.
It's a little tight, but with a light, on the back side of the Score Motor
is the armature's tail that slides in when the motor is energized, and
springs back out when de-energized. That small tail many times is dry
and a spray can free it up and give the Score Motor its proper RPMs.
Check, and I bet the Pins are in the totally reset position before the
Relay Bank energizes..
Yea, if you can make out the color codes okay, you can first jump
the #1 and #3 pins to the Jones Plug and see if that does the trick.
It probably will. It seems you have a bad spot in the Pin Deck's Pig
Tail.

The 2 wires that energize the Coin Relay are the common Yellow and a Blue-White wire.
That Red plastic button is/was to energize the Ball Gate coil if the balls didn't release, but
on Home use machines I've wired the Yellow and Blue-White wire to its switches to have
it as a Free Play button..
I have a Pin Coil for the #3 pin. You can pm me with your address, and I'll send one to
you tomorrow..