So let's be careful here. If you read what I posted, I mentioned that just because a system draws power from a circuit doesn't mean it doesn't draw power from elsewhere. The 115V system only uses the circuit in question to power a relay coil (i.e. low current draw). The primary power source for the actual 115v inverter is on its own 15A circuit. So the fact that you don't have or don't use the 115v system doesn't imply that there is massive headroom for adding devices. Again, the only safe way is to test with a current meter.
According to the wiring manual, the factory mirror has two wires. A yellow 12v and white with black stripe ground wire. These wires are part of the roof wire harness which runs along the top of the windshield, down the driver side pillar, and into the driver side junction box.
If you remove the fuse cover on the lower dash you can see the junction box. The mirror wires terminate into the 20 pin connector, 1A. facing the panel from the front, find the top right connector. It should be in a vertical orientation with the pins as shown here.
20 10
19 09
18 08
17 07
xx xx
16 06
15 05
14 04
13 03
12 02
11 01
Pin 02 should have the yellow 12v wire attached to it.
Pin 14 should have the white with black stripe wire.
If you don't have these wires in these locations then your mirror was probably wired up outside the factory. In that case, I cannot say which circuit it's on.