I had this problem for about a year. A couple of months ago I tore up my door to pin point the reason for the non-working heated mirrors. At first I thought it was bad wiring or some strange electrical voodoo, so I bought a Prelude electrical manual off eBay. Turns out i didn't need it. The problem is the switch itself.
Not sure if the problem I had is common to all Preludes, but I'll explain my situation in the hopes that it may help you or others.
Using a multimeter I narrowed it down to the switch as it showed no connectivity whether I had the switch on or off. So I removed the switch from the door and opened it up. There's like a single screw and some clips you gotta pry apart, but it's straight forward. Just be careful there's a bunch of little springs in there that may fall out if you're not holding it right. Anyway, I noticed that the internal switch is fairly simplistic and looks like a switch you find under the left and right buttons on a computer mouse. It's a micro switch similar to
these. Anyway, there's a piece of metal sticking out on top of the micro switch that kinda acts as a lever. When you press this button down, it presses on a little button which closes the circuit and allows current to flow through the switch, the LED and the mirror heaters. For me the problem was that this metal lever thingy was bent down. I bent it upwards, put it all back together and it's been working ever since.
Hope this helps.