So the ball drains and the game sits there as if it's waiting for the ball to drain? There's only one other switch that needs to work other than the Outhole switch to fire the Outhole relay:
Shangri La outhole relay (resized).jpg
Is the switch on the score motor (Index cam, C or 3rd swtich) clean and closing properly?

Or is the Outhole relay working just fine but nothing else happens once it fires?

/Mark

Inspect the score motor position when it isn’t working. Is the make/break switch in the NC position? Is the outhole relay energized? If you close the outhole switch does the relay energize momentarily?

Does the outhole relay fire when the game freezes? If not, the problem is probably somewhere in this path. It's intermittent so it could be a dirty switch, a bad connection through a jones plug, a cold solder joint or possibly the score motor isn't stopping in exactly the right position (which would close the NC switch on the Index cam).

The easiest thing to try would be to clean and adjust the two switches to make sure the contacts are swiping when they close, not just barely touching.

If you're comfortable working in a game that's plugged in, carefully lift up the playfield next time it freezes and poke at some things in this circuit (switches, solder tabs, jones plugs, etc.) with a wooden stick to see if you can get it unstuck. To be safe, no bare feet, one hand in your pocket, and don't lick anything

Hi austinmgrant +
I started to play pinball in the very late 1960ies - Shangri La was my first love. By now I have one --- one of the best 2-inch flipper-bat pins. We may come to talk about "Extraball" feature --- see the JPG: Along "my brown X" we can make an Special-Replay - well, we seldom make an Special Replay --- to troubleshoot on Your problem: The "my brown X wiring" is not good to help us.

Whenever there is a "seldom fault" I like to use Test-Lights*** --- MarkG : I have taken Your JPG (post-2) and added "blue" Test-Lights***. We toggle-off (respectively unplug the main power cord) - hook-on permanent one or more Test-Light(s)*** - we plug-in (toggle-on), start a game and play --- we play many games and have an eye on the Test-Light(s)***. Long wires on the Test-Lights - coming out of the open coin-door, Test-Light(s)*** (insulated) laying on the apron. We play and play - when the seldom fault shows up - question: What did the Test-Light(s)*** do ?

See the JPG - mounted "blue-5": The Test-Light*** must be lit all the time,
"blue-4": most of the time lit - "unlit when the motor turns for some reason",
"blue-3": most of the time lit - "unlit when the motor turns for some reason",
"blue-2": lites up when the ball-lost enters the outhole,
"blue-1": lites up when current reaches the coil on outhole-relay.

The difference "test-blue-5 versus test-blue-4": We test the switch on Score-Motor-Ind-C.
The difference "test-blue-4 versus test-blue-3": We test the connecting wire of color-BR-B.
The difference "test-blue-3 versus test-blue-2": We test the Outhole-Switch.
The difference "test-blue-2 versus test-blue-1": We test the connecting wire of color-BLU-Y.

No need to make You 5 Test-Lights*** - One is enough - You may start testing "hooked-up as blue-2" - EVERY TIME You loose a played ball and it enters the Outhole: DOES the Test-Light light-up ?

Test-Light*** - when You can buy 24VAC lamps / bulbs: Buy --- otherwise: SteveFury shows "12Volt car-bulbs put one behind the other make an nice Test-Light***: https://pinside.com/pinball/forum/topic/reading-gottlieb-schematics#post-2634425 Greetings Rolf

0Shangri-La-pinside-OHR-Work-A (resized).jpg

Hi austinmgrant
this post is only theory. Maybe the text (JPG in post-2, drawing of Index-Cam) "Outhole-Relay DELAY" is confusing - what means DELAY ?
On Shangri La we may loose the ball through on Outlane. If it is lit: We get 300 points. Making 300 points needs the help of a turn of the Score-Motor (180 degrees). Making 300 points takes some time. IF (if, if) the ball rushes through an Outlane and enters the Outhole: The making of 300 points has not completely done. Nice invention of the Williams engineers - making 300 points have the motor to turn - AFTER making the 300 points: The motor runs out, reaches Home-Position - NOW the switchstack on the Index-Cam moves back - the part / switch Index-C closes - NOW the Outhole-Relay is allowed to pull-in to do the stuff needed "when a ball is lost". Greetings Rolf

The switch that is on the other end of the make/break we are looking at provides 24V to the score motor to let it complete its rotation.
Give it a good clean/filing and make sure it is making good contact. It is the one labelled "Motor Run" in the index C switch diagram.

Another possibility is that the score motor rotor isn't dropping out as quickly as it should. If you remove the metal shroud that covers the motor gears you can get a better look at the rotor. It's the copper cylinder with a small gear on one end of its axle.

When power is applied to the score motor, the magnetic field created by the winding and the stator (the stack of sheet metal surrounding the rotor) pulls the rotor into the hole in the stator, engages the small gear with the next gear and makes the rotor and the rest of the score motor turn. When power is cut, the magnetic field goes away and a compression spring on the rotor's axle pushes the rotor out of the stator which disengages its small gear and effectively makes the score motor stop suddenly. It's a simple but effective clutch mechanism.

The rotor and its axle often get coated with grime which makes the motor work a little harder, but also makes that sliding back and forth (engaging and disengaging) motion sluggish. If the rotor doesn't disengage immediately when the score motor power is cut its angular momentum keeps it and the rest of the score motor turning enough to run past the expected stop position. Sometimes the motor will overrun enough to close its own run switch and run right into a second cycle. A fatigued return spring can have the same effect.

You should be able to briefly short the normally open Score Motor Run switch (from reply #2) to get the score motor to start turning. Then watch the rotor as the switch opens at the end of the cycle. Repeat that a bunch of times to see if the rotor ever looks sluggish when returning to its rest position.