I've been screwing with these things since the '50's.
If the guy took as good care of it as you say, he probably drained the gas or, at least, put Stabil in the tank for the winter. I doubt that varnish is the problem. If fact, the only time I've had a problem with varnish is when a implement was put away and left long enough for the gas in the tank and carb to dry out (years).
3 things I can think of:
It is old enough to have a condenser in the ignition system. If these short out, the engine will idle but, when you try to accelerate it will stall. Need to pull the flywheel to get at it. They're cheap, Don't try to diagnose it, just put a new one in and throw the old one away.
I've seen older carbs with a rubber diaphragm under a rectangular cover. They act as a fuel pump and when they crack, the engine will not run well or not at all. 10-12 years is about as long as they last.
Check the carb to engine mounting bolts and gasket.
Good luck, Jim