You actually also have to remove the door panel on sedans to unplug the old wire and plug in the new one. On my buddy's older generation 94 the plug was inside the "sail panel" that 98CoupeV6 mentioned you need to remove.

And removing the door panel takes more time than the mirror itself. I guess you could try pulling the wire up, but you might have to take the door panel off. To do that see below: