Your advice to the man wanting to buy the 1962 Austin-Healey was only partly on target. Always good to fear the worst, but many long stored cars do very well when a little TLC is applied. The absolutely best advice for anyone new to classic British sports cars (LBCs, for little British cars) is to Join A Club. Our Healey club in Atlanta has Tech Sessions, where the person needing help buys lots of food and drinks (usually nonalcoholic) and the other club members bring their expertise to help fix the car (when they are not eating), and many members know a LOT about their cars. Now to your caller’s dream: I have a 1962 Austin-Healey 3000 Mk II with 188,000 miles on it. It only quit once, after pulling into a gas station and running over a nail. I did have the spare so no big problem. HOWEVER, I stored it for 7 years and found two aging events happened: carburetor connections leaked (cracked rubber) and steering box leaked its oil. So ALWAYS check all fluids before doing anything to the car, and replace the oil (as you advised the guy from Sitka). And replace any hoses that look cracked or worn.
Otherwise, the old LBCs are great fun and usually overdesigned for today’s roads, so are pretty reliable.
They weren’t all that reliable when they were new. Why would one be at 50 years of age?
Keeping that in mind, I’ve been an LBC owner since 1967, and it wasn’t new then.