I have a 1983 Trek 720 I did a resto-mod on. The headset is a Tange MA-60 1" threaded headset taken from another Trek. I had a bike mechanic set the top and bottom on my head stem with a headset press. I did the rest. I've been doing lots of brake testing and when I really really reef down hard on the front brake, sometimes I get a weird sort of soft 'cunk' like the fork is wobbling in. Not really wobbling, but there is a feel of something. It might be the brakes themselves, or the headset. If it's the headset, I'm guessing either my headset is not tight enough, or its pair of caged bearings is suspect and should be replaced with loose ball bearings. Any suggestions?

Did the fork race drop on or need to be hammered on? It should be the latter.

Tight coming off for painting, and tight going back on. The mechanic set that too with a tool. It is tight tight tight to the steerer tube.

What type brakes?

If rim brakes, then sometimes the seam where the rim extrusion is pinned together will be a little out of line and there will be a little bump felt in the brake lever every wheel revolution. More common with new wheels, but a big bump and incorrect spoke tensions might let the joint get out of alignment on a old rim. Not usually a issue. It'll wear in after several rides when the brakes get used enough. Or sand it smooth.

If disc brakes, then check the rotor center lock and/or bolts.

You are sure there isn't play in the headset?

Not rims. Cantilever brakes. Headset seems like there is no play, but maybe I'm not wiggling it hard enough to test. Hard to test when riding, I tried to cup my hand around the top then bottom by the fork crown when it happens to see what I feel, but that's too hard for me to do when riding.

I will be doing an entire brake change later on, we'll see if that solves it.

Lift the bike by the seat so I dangles front wheel low. Hit the front tire with your fist aiming for the BB. A loose headset will clunk.

wrap your hand around the top of the headset, covering the upper and lower threaded parts' joint, as you test-rock it... you can then feel a tiny bit of slop that can't otherwise be felt as a "clunk".
whether it's a brake clunk, or headset clunk, or even WHEEL clunk, can then be determined.

sometimes all it takes is a 1/16 turn of the adjustment to get it perfect... or less.
minor issues with seal placement can cause a false drag on the headset, and the plastic seal won't clunk during a "bench test".. BUT your hand CAN feel the motion...

So old there’s no plastic seal

No more advice than above, but I have a 1983 Trek 520 and I love it. (Coincidentally I'm having headset problems of a different sort.) But I think it's pretty cool you live close to where the bike was made.

If your front brake arms have some slop from looseness or wear you can isolate their movement by applying the front brake while rocking the bike back and forth. There is usually a little flex in the arms but its easier to see loose fitting parts this way. This can cause some clunking and squealing brakes from the loose brakes vibrating when applied. If the brakes check out OK then it's most likely the headset so you should first check the tightness/preload of the nuts and even though the mechanic used proper press tools for the cups and crown race, if they're just slightly not squared it can cause some clunking that can't be adjusted out.