The volume of my speakers going down by itself and going back again in a minute or two

Your new to you 20 year old pre and power amp might need a tech check.

I had the same thing happen. Then I realized the dog was stepping on the remote. All 7 pounds of him. 

Overheating? Turn off lights and look at tubes for red plating.

I'm thinking the possession thing. 
 

Both channels are experiencing the volume change? While I have never heard of such a thing... if it is in one channel, I would suspect a tube. ARC is really well made... so the most likely culperate is a tube.
 

ARC will have one tube for both channels or two or more per channel. If the problem is in one channel. Then switch the 2 or four tubes per channel in the Amp first and see if the channel changes... then try in the Preamp. If it is both channels, get a replacement and se if it goes away. 
 

You write: "I just upgraded a used Audio Research tube Preamp and a power amp." Do you mean that you upgraded to a used Audio Research preamp and amp ... or that you had the used preamp and amp upgraded?

Also, as obvious as this is, if the used equipment is new to you, do you have your old equipment? That would help isolate the problem. 

If you haven't already, you might try playing Mike Oldfield's Tubular Bells. What do you have to lose?