1973 Coup De Ville - Diagnosing malfunction of passenger side rear signal/brake bulb

[Caddy_Hooligan]

I recently acquired a 1973 Cadillac Coupe de Ville back in July, 2023.

PROBLEM:

When I took possession of the vehicle, all of the exterior lights (head lights, front signals, rear running lights, rear brake lights, and rear signal lights) were functioning perfectly. The interior indicator (for lights on, braking, and rear turn signals) just above the rear bench, above the rear window, and mounted at the rear of the headliner were functioning perfectly. Out of nowhere, just a few days ago, I had a friendly driver pull up next to me and inform me that my passenger side brake and turn signal lights were not working. The rear running lights were still working on both sides. I then noticed the passenger side internal indicators viewable from rear view mirror were not lighting up when braking or activating the passenger side turn signal. 

QUESTION / HELP NEEDED:

I'm new to working on cars (new/old) on my own, but am mechanically savvy.
How do I go about diagnosing what might be causing the above problems?
What are some of the reasons any of you have seen this happen?

NOTE: I have the original "Cadillac 1973 Shop Manual", but I'm not able to get the guidance I need from it. I was going to just try to replace the bulb, but the manual is telling me that in order to get to the bulb, I need to remove the rear bumper in order to then remove the tale light housing. As I'm sure you can understand, I don't want to go down this road if the bulb is not the problem. 

Edited April 2 by Caddy_Hooligan
Typo and Adding Model/Year to title of post

[Logan]

That car is using a GM / Saginaw steering column. Used forever from the late '60's till sometime in the '90's in GM vehicles. 

Not a common problem.....but a known problem that could happen. A worn out turn signal switch. 

Pretty much all the lamp wires have to go thru the turn signal switch to accommodate the turn signals and hazards function.

If you search on Google you should be able to find out lots of info on worn out GM / Saginaw turn signal switches.