How do I break in a tube amplifier?

30 min warm up time is usually about right for my tube monoblocks and preamp. For the first one hundred hours or so I would leave it on continously and play music when you can. It will break in the fastest this way, but by then the electronics should be well settled in. If you're lucky you will get to be present when a break in "bloom" plateau appears; I recently had this happen with a new preamp and fortunately I had audiobuds over for a listening session when it happened. Everyone went "whoa!"
Tubes are amazing.

Was told by an Audio Research technician to wait five minutes before restarting a tube amp

Did Audio Research tell you where you should wait? Can you pace around or should you just sit there? Leaving a new tube amp on for one hundred hours continuously is fine if you're going to sit next to it...this should be easy if you have 2 kids as they can visit you from time to time to see if "the insane dad" is still breathing. The "bloom plateau" is often only a power surge, radiation leak, or stomach virus, group hallucination included, but your results can vary. There is no "3 hour wait" rule by the way, so feel free to ignore that one, and anything I or any of the other certified nut jobs around here say.

Ditto to Wolf garcia's comments!BTW I have had less problems with tube gear than solid state! Once in a blue moon you might have to replace a tube but that's about it. Enjoy and don't worry!

Considering I can't leave the tube amp on without speakers connected and I only have one pair of speakers that need to be connected to my home theater system the majority of the time it'll be hard to leave it on for more than a few hours at a time. Especially, considering I can't leave it unattended while it's on.

I'm starting to appreciate solid state more all the time :-)