All the fast idle lever does is move the cam in the cable splitter box in front of the air box a little, so the idle revs increase as both throttles are held open a little.
There is a little tiny ball bearing in a channel in the switch gear on the left handlebar, and a return spring in the bowden box (the little box that splits the throttle cable into two cables under the battery box area)
The little ball bearing fails quite easily and it's a bit of a pig to replace, and quite expensive (especially if you follow what the computer says you have to do and replace the whole kit with OEM parts)
It's also unnecessary.....just start bike and hold it on throttle at about 2 k revs for 30 secs and it should have warmed up enough to tick over at idle after that.
I ran for a few years with one of my daughter's hair bungy things wrapped around the fast idle lever to give it the required friction against the return spring, but once you have the bike tuned properly, you don't really need it in the UK at least.
The other option is to adjust the idle speed on both throttle bodies so it's at 1200rpm or so, maybe up to 1500rpm......it won't hurt anything but over a long period, if you sit at lights or something a lot, it will obviously use more fuel, and in the summer, you want the idle lower so it gets a chance to cool a bit more.