laurieb said: Well, intermittent it is.
Check the P/N switch output to the ECM for intermittent connection. (This is separate set of contacts NOT associated with the starter contacts. Even if it cranks reliably, the ECM contacts may not be 'set'). If the ECM doesn't know the shifter is in Park, it may not properly 'set' the IAC for start-up.
It is an orn/blk wire on pin B10 at Connector 2 of the ECM. Back-probe this connection with a VOM connected to ground. (A12 blk/wht, C2 is an ECM ground. It's difficult to establish a good ground in a Corvette for test meters).
With key on, engine off, in P or N you should read 0-volt. In any other shifter position you should read nominal 5.0-vot. Wiggle the shifter in Park and watch the meter. If the voltage isn't a constant 0-volt
throughut the "wiggle-range", move the shifter to where you get voltage in Park, and try to start it. If it cranks, you have a worn P/N switch assembly that allows the starter to operate, but not send the 0-volt signal to the ECM.
As a further diagnostic, note where this occurs. It will be either at the forward, or aft end of the shifter position. Note which one is "wrong". When starting the car, make sure the shifter is pushed to the "correct" position. If the intermittent low-idle is gone when doing this, you figured it out.