Hi!

Any suggestions on what I might look for to repair this?

Sure, I'd start by looking at the capacitors in the set. They may be
failing. Starting with the ones in the power supply would not be a bad
idea.

Remember that a TV set contains hazardous voltages and may well
maintain a charge after you've turned it off and unplugged it--
especially if the set is malfunctioning. You have to be on the lookout
for high voltages AND line voltage. There's also the risk that comes
from an implosion of the picture tube if it should be abused while the
set is apart.

William