Here are some waveforms in the sync circuit.
First, the output of the sync eparator.
That signal goes through a 0.05uF cap then through a long wire to the deflection circuit. The red pointer is this cap.
The scope is hooked up to the other end of that long wire.
Could it be picking up hum?
Also, note that the sync separator is right next to the power supply. No shielding on the tubes.
Here's the other side of that cap
Here's the resulting sync signal on the grid of the horizontal multivibrator.