First off, congratulations!
As to burn-in, I always just play the amp like I would any equipment. So, no, I don't keep track of the hours in any way in particular, other than maybe a calendar.
If you are interested in hearing the differences as it burns in, play a piece you are very familiar with, then put it away for awhile. Bring it back out after you reckon that the amp as been used for a number of hours, then play it again.
I certainly do not pretend to know the mechanism(s) at work here, but I can say that I have experienced the changes; I recall one set of output caps that sounded good at first, then went through a stage where they were so bad that I almost yanked them, before they settled in to sounding just remarkably good, and they sound great to this day.
As a rule, about 50 operating hours (playing music) seems to be the point where most of the amp gets burned in. There are many exceptions, of course, with some parts taking much longer.