It could be a few things. Check all the things.
Thermistor is the only thing that I can think of… Hopefully tightening it works. It doesn’t happen unless the print head is in motion, which makes me think that’s the problem. Otherwise, the temperature is stable and completes PID tuning without issue.
It could be a loose wire, or a one that is about to snap off. If the cable is bad or on the way out, it could easily be screwing with the resistance measurement. I wouldn’t think that just a loose thermistor could cause that mess of a graph, but who knows.
It’s the motion bit that you mentioned that gave us just a little more data.
If you can isolate the wire for the thermistor, jiggle it around at different points to see if you can replicate the rapid temperature changes.
