Stumbling can easily over-extend or tweak something, or they can whack a toe or clip themselves without you realizing it. I would assume the limp is secondary to the neck, but not to be ruled out as a sign of something having been tweaked.
You can spend the money hunting for zebras, but it sounds like this guy is having trouble compensating for whatever he’s got going on. It’s really common for these horses, and exceedingly common for neck issues to cascade into other problems. Sometimes it’s due to compensation and sometimes I think there’s an underlying connective tissue or some other issue we can’t yet test for or diagnose. I am sorry for anyone who has to deal with this 
The vet may have some insight, but I don’t think it’ll be a “it’s actually X issue and nothing else” kind of revelation. As nice as that would be! As you may recall, I have one of these horses and it’s always a game of tempering my hopes that “just one more thing” could fix him 100%. He is who he is, and he’s chilling in retirement.
ETA: I’d get the vet to flex him at least, maybe X-ray if a joint pings pretty off, but if so I personally still wouldn’t go into it thinking it’s the leg and NOT the neck. It’s likely both. BTDT and the horse still has neck/spine issues.