EGT gage oddity; stuck valve, other??

Folks, I'm hoping you can help me diagnose an odd EGT gage behavior.

Background: 1965 Aircoupe with Continental C90-16F engine (has vacuum
pump). Plane based in N. California so freezing temps not a factor
(pre-heat not needed nor used). Has both a CHT and EGT on different
cylinders, with the two-needle combined gage in the cockpit. The CHT
works fine, the EGT was working fine until 2-3 months ago.

Now, the EGT fairly consistently acts like this: it reads "normal" on
cold start, taxi, runup and takeoff. Climbout it reads around 1200
deg F. like it always did. Then, after a few minutes, it starts to
fall, and within maybe a minute or two, the needle quivers at the
bottom of the scale. It never recovers from that; but at next flight
a week or two later the same behavior happens. I never notice any
change in engine performance or sound.

Would a stuck exhaust value cause this? But wouldn't I notice
something from the engine? What else could cause this repeating
strange behavior? Maybe it's something heat related?

Thanks,
Bob