For a Tek TDS210 I repaired years ago there was specific instruction in the Service manual for backlight repairs.
It stated:
use a 100:1 probe and expect a 1250V p-p output @ ~60 KHz.
If the voltage was present but still no display, replace the display.I now use this MO for backlight investigations:
The switching frequency & primary voltage can be safely confirmed before the step-up transformer and HV presence can comfirmed using any scope probe as a "near feild" probe.
No contact needed, just a close presence of the probe will pick up the EMI.
Sure there are controllers that shut down the backlight if something is amiss, but thats another issue.
BTW the Tek as described above had NO controller, just a simple bipolar push pull inverter with a knackered timing cap.