It is usually easier and safer to just change the high voltage capacitors and the diodes in the DC restorer if a problem is suspected there. As Sarasir points out, a high voltage is needed to test them adequately for leakage and I figure if I had to pull the parts to test them, I might as well install new ones anyway unless they are expensive or difficult to find.
Before going that far unless there was an obvious problem like a low voltage short in one of the diodes or capacitors, I would certainly test the power supply voltages for level and ripple and do the z-axis calibration procedures including the grid bias adjustment. Then I would take a look at the output of the z-axis amplifier to verify that it is responding correctly.
When working with the z-axis circuits or if there is a problem in that area, it is a good idea to defocus the CRT to prevent damage to the phosphor.