Another way is to leave the door panel intact, remove the power
window glass, (flip tab up or down in center of mirror between mirror
and outside case with something thin-see archives) then pull glass
away and unhook the two heater wires from the glass.

Now remove motor assembly with 4 phillips screws.  Pull out wires
from back of motor assembly (color coded).

Now remove black motor mount base with smaller phillips screws.

Then pull entire mirror away from body and carefully fish wires
through mirror base one by one starting with smallest wires first
ending with largest wires (pick tool helps here).

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Installation is the reverse, note that when putting together fish
largest wires first through the holes. Don't forget to fish wires
through the rubber gasket before the mirrors....learned that one the
hard way.