Ahh vacuum systems. ;53
Provided the light in questions mechanism is OK, not tight etc, etc, with motor off there is only so much vacuum stored in the reservoir tank. A faulty vacuum check-valve near the carby or leaks in the system will cause vacuum to leak out very quickly once engine is off.
Any vacuum leaks can cause the problem. Including the vacuum switch on the headlight switch, A/C-Heater Controls, Brake booster, Cruise control if fitted, Kick down on auto if fitted. When I re-did my system with an after market check valve and all lines replaced and no leaks I can close my headlights with the engine off and partially open them back up again.
It's a fun job chasing it down.
All of this based on what I found with my 77. Not to be taken as gospel, but hope it helps.