Measure the draw on a power right . Be sure its 3/4 to 1 A
IIRC. ( see label)
May be a weak breaker.
Next would be the big oval cap across the p xfrmer.
Check the low ohm, usually 1.5 at the horz out base.
Too much beam current can also cause this but never seen
it on a Zenith.
If it is something dead shorting normally before tripping
you will get a very loud 60cy hum.
BTW is this an EFL set ? if so it will have a PCB on the CRT
socket ( 9-120-## ) and some other changes.
73 Zeno