How do I break in a tube amplifier?

Note that it's OK to leave it unattended when it's not on. Waiting 3 hours to turn it on after turning it off is silly. Tube amps, if designed and built properly, are tough little buggers and don't need nearly as much pampering as many think. My experience says you should simply enjoy the damn thing and it will "break in" from listening to it, and might last longer than you with less upkeep.

I was going to verify that I could leave it alone when turned off as I would rather have an iPod if I have to carry it with me.

I'm aware that heat cycling the unit has the potential to shorten it's life, but once it has reached a steady state operating or ambient temperature it seems that any additional time would be unjustified. I currently have my system (that includes home theather and stereo components) setup to leave everything turned on once it is turned on and then shuts everythign off a single time rather than cycling everything when switching sources.

I shouldn't have any issue abiding by the leave it off for 3 hours before turning it back on again "rule", but with two small kids I'll have a difficult time finding 3 hour windows for listening where I will be available continuously so I guess I'll just have to risk it.

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.