Thunk from the bottom bracket
 

Ok, here's a baffler. Unknown year Azuki 10-speed (2x5) 27", with 3-piece crank.

Looking at the crank from the right side, this occurs between 6-9 o'clock, and only when high torque is applied to the pedals. And I feel it through the right pedal only, not the left (despite the torque coming from the left side at that part of the revolution)

BB is solid, no slop that I can make out. FD isn't hitting that I can tell. The front chainrings are not perfectly flat, and do wobble slightly, as does the ring guard, though I can't see anything that they may be hitting, either.

Kickstand was removed first thing, as it was my first suspicion.

So, I'm stumped. Anything embarrassingly obvious come to your minds? :)

When was the last time you replaced the bearings and repacked the bottom bracket?

How tight are your crank bolts? Were they ever loose enough to make noise? A stripped/mushroomed crankarm can do this.

Overdue bearing maintenance is not going to produce a clunk at a fixed point every time, but there is a likely candidate. Fixed cups sometimes loosen enough to shift under pressure, but not enough to detect when doing the typical "is the bb loose" check. It's common to feel it mainly on the right, as there's more direct pressure on the fixed cup from that side.

Remove the right crank arm and put a wrench on the fixed cup (tighten counterclockwise). If it does move that's the problem. Before cinching it down loosen the lockring and back off the adjustable cup. Now tighten the fixed cup solidly and finally adjust the bottom bracket. Of course it can't hurt to overhaul the BB.

Although I have no wrench, yet, and the right cup will not turn by hand, a visual inspection of the area shows that the right cup is not flush against the frame, so this may very well be the issue. Off I head to the bike shop, to expand my collection of tools.

Thank you, everyone, for the suggestions. :)

i'd bet it's the bearings in (one of) your pedals. hold the crank steady and try to wiggle the
body of each pedal in turn. one of them will have some play. if you remove the pedals, hold
the cage and try to wiggle the spindle, the play will be more obvious.