What I've seen often is a subharmonic flicker, so a fraction (mostly 1/2) of tge mains frequency. It happens, when the cathode is in such state there are few spots equally attracting the root. The thing is, the arc technically extinguishes every time tge current drops to zero (so 100/120x per second), it has then reignite again for the next halfcycle. So all this is about is which spot is the most favorable cathode to ignite the arc and become its cathode root for that half wave. The flicker uses to be caused by the arc root "dancing" on the cathode  the arc root settles at different spot at each other power cycle, not the same one. It is normal to happen from time to time for a few hours. It require really very precise balance between those spots on the cathode, which does not last long (an electron emitter barium atom boils off the place or one edtra seeps in and the lamp becomes steady again). Although the total light output does not flicker, the arc moving cause the light distribution to vary so unless there is a really ideal light diffusor, the arc dancing does appear as a flicker from most angles (each arc possition yields slightly different beam pattern).
Then the one where the arc was the last time becomes the tiny bit less favorable for arc reignition than the other, the arc just ignites on the other spot. And the next cycle the second one becomes the tiny bit less favorable one, so the arc ignites back on the first one. And back and forth, so the arc root alternates between those spots. What causes the place where the root was the last time less favorable? I don't know exactly, one possible hypothesis could be it could be the Ba on the surface is pushed away by the heat wgen the arc is there, so then the next cycle that spot has lower emission so the arc starts on the other spot. But as the second cycle it is a bit colder, the Ba has the chance to seep back but the other spot becomes the more depleted one, so the 3'rd cycle the first spot has the higher emission so "wins" the arc root back and the cycle repeats. We are talking here really about very minor variations, a single atom present/lacking on (moving in/out from) some key spot could be all the difference between that spot "winning" or "losing" the arc root for the cycle...
