if you go download:

ftp://bama.sbc.edu/downloads/tek/545...%20545a(2).pdf

you'll have a service manual.

You probably should replace any of those black tubular bakelite
capacitors.. They tend to get anywhere from slightly to horribly
leaky. Any leakage over a microamp will mess up the grid biasing.


see the next to last page for the CRT circuit.

The brightness circuit has many high-megohm resistors-- thesetend to
drift in value over the decades.

Also around the intensity control there are several capacitors in the
C82x range -- replace them. They might measure okay under 1.5 volts
from your meter, but leak badly when under high voltage.