Checked out my 53310A a bit today. It's a little dirty and there's some burn-in on the CRT, but still looks good. Man it's bigger than I was expecting. Much wider than my 8560E, but fortunately not as long.
The listing showed that it was failing the trigger light test for the A2 board. Sure enough, it did that when I ran the self-test. Checking the DAC parameters, the offset looked like it was at default values, so I let it measure and set new offset values and bingo! All tests pass now.
After taking these photos, I noticed that the first pic shows "ref error" in the bottom-right status area. It was the first time I saw it. Normally, it says "ref int" and when I turned it on and off a few times, the error didn't return. Upon leaving it for a while, it shows "ref error" again at first power on and eventually switched to "ref int". So, it seems that it needs a little time to lock onto the internal clock reference.