My passenger side started doing this a month ago too. Not sure if it's the cold weather, but if I press it on or off, it sticks in and then 5 seconds later it clicks as it pops back. Still works though.
As with the instructions, inserting something between the rectangular lens and front edge should disengage the clip, you shouldn't have to pry it much if at all if you use a suitable wide tool or plastic card. then you can see the screws. The panel should then pull down with fingernails starting at the front as it is only held in with spring clips at the sides and barbed pegs at the back.
I haven't got round to checking the back of the switch yet though.
I also slipped some of these into the mirrors which are much brighter...
http://dx.com/s/171856