Here's some things that are a bit more esoteric, but might lead to the hint of what's up:
1. On the centerstand, jack the front wheel up off the ground. Maybe have a friend sit on the bike, and put it into gear so it won't roll toward you when you do this next (tricky) part: grab both front forks and push toward the bike and pull back toward you (the second part can pull the bike off the centerstand, hence the friend...) several times to see if it gives, or 'clunks' a little bit. What you're looking for is: either sorely worn fork bushings, which are right at the top of the legs, just below the seals, or one or two loose alignment tube(s) inside the lower. There is, on most K0 and almost all K1, a small socket-head bolt in the center of the arch of the axle crotch on the end of the forks. This bolt has a copper (or aluminum) washer above it, for a seal. If it is loose, the forks can wiggle, and clunk. This often also makes them leak fork oil at the axle. If you have forks with no bolts on their axle-hump end, then the tube was pressed into the lower by Honda: if it has come loose, this usually is the end of the fork leg because it cracked inside to let this tube come loose. This isn't a a terrible thing, as any other K0/1 and K2 before the "anti-beeper" button (left handlebar switch) disappeared has fork lowers that will fit your tubes.
2. The K0-K2 early bikes often lacked drain holes in the lower frame tubes, right behind the engine bolster bolt (behind the points cover), and/or they got painted shut. This can let the frame rust and rot right there, which makes the whole bike accordion front-back-front-back, causing an apparent wheel-hop sensation as the forks alternately compress and release. Use some slip-joint pliers, maybe wrap the frame with cardboard to protect the paint, and squeeze the frame tubes, right behind the front bottom mounts, to see if the frame squishes easily. If so, it needs a frame repair, pretty quick(!).
A distant 3rd option: guys who used to chop these bikes often removed the 2 "extra" backbone tubes between the tank's rear crossmember and the steering neck. They wanted a "lighter" look. If they followed this with extended front forks, the whole bike would "caterpillar" its way down the road until about 30 MPH, and you had to use only the rear brake to stop, or it would steer itself wild upon braking. I would not test-ride them around a corner when they came in for service, as they flexed like a rubber band in a turn. Are all 3 top frame members in place? Or, if it has a "frame mod" kit, are the end clamps of the insert portion(s) nice and tight?
