Both of these are on different fuses so it's probably 2 isolated problems.
The mirrors are on fuse #8 (10A) under the dash, but both mirrors would go out not 1. The switch gets power and then sends it to the mirrors. So if the right mirror works, It's either the switch, wiring from the switch to the mirror, or the mirror. Not in the wiring from the battery to the switch.
The cig lighter is on a fuse in the engine compartment. It's a 20A and also feeds the power seats. If the power seats work, than it's not the fuse.
Rick