If you've opened and closed both widows using the key fob, the chances are that the switch is indeed faulty. I had exactly the same.
Using a decent flat blade driver or metal rule, gently edge the switch assembly out, unplug, take indoors and carefully unclip the top half of the assembly (you will have to remove the plastic switch that selects which wing mirror to move, it just pulls upwards). Inside the switch box there's a rubber pad which makes contact with the pcb contacts underneath, this is operated by 4 flat pieces of plastic (like pistons) which are actuated by the window switches - don't lose these!. Pull the rubber pad off of the pcb and you will probably see some dirt or contamination on the contacts, give these a gentle clean with a glass fibre pen or emery cloth etc then wipe clean. On the underside of the rubber pad there are 4 contacts, clean these as best you can. When reassembling make sure you locate the rubber pad correctly on the pcb by locating it in the 2 holes (I used a cocktail stick to make sure they were pushed fully home). If it's not located correctly this can give rise to one window affecting the other.
That's it, might sound a bit complicated but it's a 10 minute job.