Joe:
I’d recommend joining a local Triumph club if it’s possible, even if you have to drive a few hours once a month for the meetings - tons for free advice and assistance for the price of a beer and a slice of pizza.
My TR7 hadn’t been driven for a long time like yours. Before even buying a battery or trying to turn over the engine...it was recommended to me to test the vacuum advance/retard on the distributor. It was excellent recommendation!
A TR7 (and Triumph GT6) will over heat if the vacuum advance/retard can’t hold a vacuum. The car will also not pass SMOG inspection if you have one in your state.
You don’t need to turn on the car…just connect a vacuum pump to distributor, give the pump a few pumps, and see if it holds a vacuum…if it doesn’t… try pinching the hose and if the pump still holds no pressure…you have a bad pump…if it does hold pressure but not after you release the pinched hose…you got a leaking vacuum advance/retard.
Unlike a GT6 the TR7s vacuum advance/regard is not available and cannot be rebuilt…you’ll need to fine a working one (used) if you plan to make that trip to Boston this summer…and not have the car over heat on you

until then you’re limited to little drives around the block with no traffic…on cold mornings.
Since your only solution is to fine and buy a “used†working one…you’ll be visiting swap meets and looking on line…make sure you can return the vacuum advance/retard if you buy it one online…carry around a pump if you visit a swap meet, and test it yourself.
Its amazing…someone will look you in the eye and say it works…then take it home to find out it doesn’t…then not want to return your money.
Do not believe anyone who says they can be rebuilt…THEY CAN NOT! Other Triumphs can but not TR7s…that I know of.
Good luck
-Vino
Ps…not a bad idea to have a working spare with you on a long trip...oh and let me know when you're headed to Boston...i'll meet you there
