Pull the triangular grey plastic trim off of the inside of the door, where the mirror mounts. You'll then see three socket head screws that hold the mirror in place. Remove those and the mirror will come away, exposing the white connector block for the loom. Disconnect that and have a close look for green corrosion on the contacts. A squirt of WD40 and making/breaking the connector a few times usually cleans them up. Try the mirror again after you've done that. If it still doesn't work, it means heating up the small (lower) mirror with a hot air gun or hair dryer to soften the glue that holds it on. Gently prise the mirror away - take your time as it's easy to break - then you'll have access to the screws that hold everything together. There are other contacts inside the mirror that can get dodgy because of corrosion.