Hi Dave,
I don't know if this is relevant for your case but I have a Keithley 2001 on my bench right now. In that unit
ALL the Nichicon UVZ series electrolytic caps were leaky on the bottom were the leads penetrate the case. These caps are used everywhere on the analogue as well as on the digital board. In my case, this lead to a relay chattering on the analogue board. Judging from the design of the case, our instruments might be roughly the same age. Maybe yours has the same problem but with different symptoms.
You can find more on my meter including an Image of some of the damage I just uploaded in this thread:
https://www.eevblog.com/forum/testgear/keithley-2001-defective-relay/