Accelarating RPM

Hey- Im new to KZR and a relatively new owner of a 1982 KZ1000.
So here's my question: I have been dealing with some big rpm issues- I thought I had it nailed down- found a vacuum leak at the intake manifolds so I changed them out- it's got a new starter solenoid( to that that effects it but thought i'd mention) Prior to putting th new manifolds on i'd start it up and the rpm would rise quickly once the bike was warm- did the change fired her up- it idles fine for a good 10 minutes- I adjusted the idle screw had it sitting pretty and solidly at 1200 rpm. I rode for about 15 minutes super smooth and then my rpms start shooting up again- my bike is accelerating without touching the throttle- but throttle doesn't feel sticky. Up shutting shoots the rpm and down shifting does the same... gosh! any thoughts or where I could start trouble shooting next.

I should add- i went through and replaced some hoses that had potential for vacuum leaks. It's got all new plugs. Is this a carb sticking issue- and if so why only after cruising for a second

Several things can cause what you describe. Among the more common culprits are-

Throttle cable - frayed, corroded, dirty, not lubricated.

Ignition advancer - dirty, corroded, not lubricated, broken, weak or missing springs.

Throttle shaft - dirty, corroded, bent, broke, weak or missing return spring.

With any old vehicle, a new owner should spend some quality time with a genuine factory service manual, carefully performing ALL the routine maintenance, in the exact order and using the exact procedures listed in the manual. You have no idea what has really been done to this bike, what has been neglected and what has really been boged up.

Thanks for the info

I think i've ruled out the throttle cable- it's lubed and seems to be in working order- there's no sign of corrosion or fraying
I did give the bike a once over, went through most of it- but will check the other two you mentioned and hopefully track down this culprit