Tom, I had a similar issue with one of my Lincolns. I realize your car is a Cadillac, so maybe my story will be pointless, but maybe it will help too.
On my 1979 Town Coupe-based flower car, the headlights would come on, but then go out after X number of moments, and come back on again after another X number of moments. This cycle kept repeating itself, but the other lights remained lit the whole time. I asked some people knowledgeable about Lincolns about this, and they said that a not common, but not unheard of either, issue with the Lincoln headlight switches of the era, is that the internal circuit breaker inside the switch just plain gets weaker over time, due to dirt, corrosion, and age, and when it does, it will trip fairly easily. They said that one can either replace the switch, or disassemble the switch and clean it up.
What I did instead, is I installed a relay with its own fuse to power the headlights, rather than have the headlight current flow through the switch itself. Now when I pull on my headlight switch, it trips the relay to power the lights. While I was at it, I also decided to power my high beams through a relay as well.
This has proven to be a solution for me thus far.