I had similar on my old 4/4 on the driver side rear indicator. I did the “wiggle” test on the wiring by reaching up under the wing and wiggling the wires. The earth wire was the problem. I took the light fitting off and the eatyh wire was simple rivetted to the plate and was not a tight fit. I renewed the fit , put vaseline over it and it sorted the problem. So, do as JohnV6 suggested. Check earthing.
A lot of the wiring on a Morgan is exposed and it is worth giving it a check, especially earth points.