Perhaps I did not make myself clear. The vacuum does not come from the engine. It is created within the switch cylinder when you actuate it with the handle. I just went in the back and disassembled an original unit. There is a piston with a leather cup, as described, working against a stout little spring which is trying to pust the piston back home against the vacuum you create when you actuate it. The bleed screw regulates how quickly this negative pressure is relieved. If your unit uses a diaphragm, I believe it is not an MGA original switch, and all bets are off.
There are no replacement parts separately available commercially for the switches . But since so many have broken at the aforementioned mounting threads, there are many used units lying about from which inner parts can be scavanged. Usually however, all that is needed is a thorough cleaning and refitting to get things functioning properly.
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon