If my memory serves, and it's the same as my 546, there's a resistor in
series with the HT supply to the HV oscillator. You can watch the voltage
across this with a multimeter to monitor the current drawn by the HT
circuit. You will see this climbing as the transformer heats up, as
confirmation that the losses in the circuit are increasing.

The other thing you can do without getting involved in measuring kilovolts
is to look at the DC conditions around the smaller tube that regulates the
HV output.

The normal failure mode is for the trace to start to "bloom" when you
adjust the intensity as the HV loses regulation and it used to take a good
30 minutes running for mine to reach this state. It never got bad enough
to lose the trace completely. It sounds like yours is a more sudden
failure than this, but it is worth investigating the transformer when any
HV related failures occur.

Cheers,

Kevin
G7BCS