The idle air control is on the left side of the engine behind a little decorative cover. It's just a plunger that a servo can move in and out to open/close a valve, respectively. Sometimes they get stuck. There's two bolts that hold the servo in, when I removed it on mine the bolts were VERY tight and Suzuki makes all their fasteners out of cheese, so very easy to strip. Ensure the plunger moves freely and spray some carb cleaner in there to remove any gunk. With the servo out, turn the key on with kill switch on, then turn it off. The plunger should suck out (open) for cold starting. When you turn the key off it should release (closed).
It's just an air valve that allows more air to bypass the throttle blades, effectively giving the bike more throttle. Older EFI bikes with a "choke" lever did this, it just was a little cam that propped the throttle open slightly more than usual.
I'm referencing a 2005 model, but to my knowledge these things did not change too much over the years.
Took me a while to check some things out, but not quite everything yet.
Was able to remove the servo, but when I test it with key on and flipping the cut off switch on off does nothing, it never moves. Also for now I don't know where the other end of electrical connector is (somewhere under gas tank, I know), but not sure if I can reach it to unplug easily or not.
I tried moving the metal shaft (what the plunger pushes I think) with fingers, it has some free play, but doesn't move much at all? It all looked very clean by the way.
Even tried ordering a new second air valve assembly, but guess what, every Suzuki parts online dealer (including partzilla and revzilla) in US is out of stock ? ... may say available, but once you purchase it will get backordered with unknown ETA, fantastic.
EDIT: Just checked ebay and found a shop parting out bikes, grabbed a repalcement valve with servo for $10 shipped, will swap and test once I get it.
Otherwise I guess at this point I should just remove the whole valve assembly and take it apart completely, clean with carb cleaner and put back in.
OK great, sounds like a plan, but what if servo-motor is dead? Need to check it again on completely cold bike to make sure... I think the root cause of problem here is that servo not doing its job at all ... I literally heard my bike only once since I got it in early July, when it was trying to rev up on its own when started cold and never did it again LOL