The knob was originally held in by two metal clips on either side of the switch body. I guess they fall out over time because mine have been missing since I got my car. First you need to pull out the knob like so:

The switch just pulls out starting from the back side.

Then unplug the electrical connector.

Now you need a piece of thin metal. Any thin, flexible metal piece would work. I had some stainless steel "label tape" that we stamp numbers into at work using a really old handheld DYMO label maker. It's thick enough to hold its shape but thin enough to bend. I used some tin snips to cut strips a little longer than an inch and as wide as the slots on the mirror switch.

The 2 slots for the metal tabs are on the sides of the switch.

Here are the metal strips that I cut:

Then I fit them into the switch.

Plug the switch back in and carefully press it into the opening, starting with the side that has the connector on it. Now the switch is securely held in place and I can adjust it while driving with one hand.

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