Yup, I'm sure that anyone owning a Brit car has experienced something like this at one time or another. It reminds me of one of my favorite jokes...
"Why do the English drink warm beer? Because they all own Lucas refrigerators"
.
Joke aside, all of the instruments will share a common ground and a common positive, so yes one connection can cause this. A wiring diagram is very helpful here.
What your experiencing is an intermittent open circuit, technically not a "short". The most likely culprit is a loose connection in the harness and to make matters worse, its probably behind the dash and the act of moving wires around to get at stuff stands a good chance of hiding the source from you.
The lucas wiring harness uses male bullets soldered or crimped onto the ends of the wires. They are in turn joined to other wires via double ended female connectors. These connectors are made from a plated sheet of hard rolled brass and are quite brittle and they will split with age. They will look fine until you unplug them since the hard plastic insulator holds them in place.
You can try wiggling stuff under the dash to narrow it down, but you may need a helper to spot the gauges while you do it. If you do "get in the ball park", start unplugging and carefully inspecting the females for splits and replace them when you find them.
I have felt your pain and I hope you can track it down without a whole lot off hassle.
Best of luck
-Michael