This car was just purchased for my daughter. I see the power mirrors do not operate. I went to the fusebox, see #19 fuse is for power heated mirrors so I looked at it. It seems fine, but when I put a test light on it there is no power to either side of the fuse holder/box. I need to follow this backwards to see why there is no power to the #19 spot in the fusebox. Any suggestions?

What year is your car so I can select the proper schematics?

https://www.askmehelpdesk.com/cars-trucks/when-asking-about-your-vehicle-303903.html

1996 4dr, GS, 2.0L 4cyl Auto. I checked fuses 19 and 34, both good. I assume perhaps, I should pull the mirror control switch out of the dash to check for power back there, but it's not obvious how that comes out without breaking something.

None of the mirrors move at all? You should test all the fuses to verify power.
If those check good you will need to check for power to the mirror connector and possibly the ground for the mirrors, too.