I agree it would be odd for both to drop out at the same time due to bulbs, possible but odd, a surge on the line or grounding issue could pop them both perhaps. More likely a relay or switch on the column?

Hit the hazards and see what happens.

Yes it is a bit of a devil to get into the rears but the fronts should be accessible via the arch if you turn the wheels. IIRC I had an issue where the cable was being scuffed by the wheel and needed restraint but that might have been a different car with my memory.

Everyone loves a Morgan. Even me, unless it's broken again.