As a side note, on doing some searching, (bumbling through a number of variations on terms to use, until the results that I was seeking showed up) I see that there are complete High Frequency generator boards available on AliExpress and Ebay, for chump change (in the grand scheme of metalwork!).
I don't have the foggiest how one might incorporate same, but the few mentions I see state that you need a capacitor to block the HF from feeding back in to the welding power source. Not anywhere near as convenient as an HF box, but if a fella were electronically skilled, it looks like a cheap way to add some functionality. Likely wire it so that the HF fires on, when a trigger is pressed, would be a start. Smarter guys than me could likely add a timer circuit... But a fella sorta needs to have a few other skills and a willingness to dick about with the stuff, if he wanted to kludge together a cruder substitute for an HF box.
Back when I first hit the interwebs, there was a lot of talk about building DC welder's out of AC only sources, using diodes that were available cheaply as surplus from the various North American sources. PA carried them, at the time, and I knew a couple guys that build bridge rectifiers from them. None of this stuff is really new, it's just a bunch of new guys trying to learn it all over again, eh?