A quick note in case it might help someone else with this common fault, plus my recommendation of a tutorial.
I recently became the proud owner of the mighty HP 8566B, advertised with the YTO unlock problem on the 2-22GHz mode only. Before I collected the unit, I tried to read up on the principles of operation (which scared me) and also did a pretty comprehensive read-through / viewing of most of the online material: Youtube, this forum, groups.io etc.
There are of course some very good and well-known Youtube videos tackling this exact problem, but in the end I found the most useful to be those from 'DKD Instruments'. They're well down the list on the Youtube search, and not at all glamorous: the video content mostly consists of a general view of the open RF unit under fairly dim light, but the presenter (unusually) gives a wide overview of possible faults and their likely causes, plus his opinion on their relative likelihood, in his (clearly considerable) experience. I found this ultimately more useful than viewing the specific 'eureka' stories that most of the other content consists of, entertaining though they are.
Anyway, for better or worse the DKD Instruments advice convinced me to park the theory and my lovingly-drafted strategic plan in favour of going for broke by just replacing C7 on the A20 board before investigating anything else at all (to be fair, other repairers also mention this specific component). It's a 10uF capacitor - mine read 9.1uF out of circuit, it looked a bit shabby but not obviously blown, so my hopes weren't high of making any difference (I don't have an ESR meter). To my huge surprise, the YTO unlock fault, previously present on every combination of span and centre frequency that I tried in the 2-22GHz mode, instantly disappeared never (or at least not yet) to return.
So that was my own 'eureka' story. A sample of one instrument isn't really significant, but I'd upvote A20C7 in the recommended investigation priority list, if there was such a thing, and highly recommend DKD Instruments' material.