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