Re: Floating rpm.. I've searched
I doubt that it's a tps, they have almost no effect on a carbed bike, you can disconnect it at idle, and nothing changes.
Initially, not knowing anything else about your bike, I would look for vacuum leaks.
It's a 97 600,so I am assuming that unless someone has swapped model years, your carbs do not have solenoids, so that simplifies things.
I heck and make sure the manifolds are tight, that the carbs are seated fully into the manifolds, that the small line on the petcock is connected to the intake #3 under the carbs, that the airbox is sealed well.
Spray carb cleaned around everything while it is running and listen for fluctuations.
1996 GSXR 750 EX AMA, Carillo, Yoshimura, Kit airbox, Keihin FCR39, Fox, Brembo, Hindle, total loss and starter less ignition, Graves, Vortex