Is this amount of record/tonearm bobbing "normal"

Rube Goldberg would be proud.

Mijo, I don’t know enough about the workings of a TD124 to cast any doubt on your explanation of the mechanism of what we observe here, but back in the late 50s and early 60s the TD124 was the cat’s pajamas for any well heeled serious audiophile, not merely “made for commercial use”. They may have been used at radio stations too, but probably because of rugged construction. At audio salons in New Haven the TD 124 was slotted into McInosh and Marantz-based systems as a matter of course.

+4 for MC, slaw, and Dover.  Watching the bottom edge of the platter as it rotates through the window for the speed sensor, it looks to be moving up and down, as MC notes.  The top edge of the platter proper (not the mat or the LP) appears to be unevenly machined.  The champhered edge changes shape a bit as it rotates if you concentrate on one point.  I'd worry about the platter first; no big deal if an LP is warped or off-center; they are nearly all imperfect.  Could be the platter is askew with respect to how it should sit on the spindle; that would be the easiest thing to fix.