For me, for 30+ years, the leaks always developed at the 6 intake/exhaust-to-head bolts. Usually just an 1/8 to 1/4 of a turn of those bolts did the trick. You have to tighten them about once a year when driving daily. Don't overtighten them or the heads will snap off when the exhaust gets red hot. The factory torque spec on those is about 10lbs lower than would be normal for bolts that size because of that exhaust expansion problem. The low tightness contributes to them unscrewing. If you end up removing them, add a little red Loktite to them upon reinsertion. The heat will burn off the Loktite, but it will help to gum up the threads and dissuade them from unscrewing so easily. There's a headpipe-to-block bracket that many Opeler's cars are missing that helps keep the intake/exhaust from wiggling up and down and encouraging the bolts to unscrew. It looks like this:
I'm not a fan of used carbs. You have no idea how many miles are on them and what rig jobs the previous owners did to them. For peace of mind, put a new one on, then you rule out every one of the 25 different carburetor-related problems that can cause you grief.
If your carb throttle shaft is leaking bad enough that it's affecting your engine, the carb is probably shot.
Based on what you said about your spray test, it's more likely that you're leaking at the carb-to-manifold gasket. You can regasket and/or you can try a quicky fixy by smearing Permatex High Tack sealer all around the carb at that gasket to plug the leak. If it works, then that was your problem and you now know you simply need to do a commonly needed regasketing. When I drove daily in my GT for 18 years, I would need to redo the gasket about every 5 years.
A somewhat far-fetched cause could be a leaking brake booster or hose. They're just a giant rubber diaphragm inside a tin can. And they're 50 years old. Not too many rubber things can last 50 years without degrading. It's a pain to remove the hose to test them though, you would either need to disconnect the hose from the one way valve and try blowing into the hose to see if it leaks or remove the hose at the booster and fasten on a temporary hose to blow through. A simpler test would be to clamp some vice grips on the hose immediately after the vacuum tree and see if that changes the engine behavior. Or try just aiming your carb spray at the vacuum tree to see if that makes the engine misbehave.
If you have an automatic you may have a leak in it's 1/4" hose also. Same deal, clamp the hose near the vacuum tree and see if that changes anything.