Key on/engine off, pump should not be running. That's why there should be a way to jumper it on to test it, similar to what is shown in the link I posted.

The IAC (idle air control) valve can get sticky. Cleaning the throttle body with some throttle body cleaner usually helps with that.

Another cause for intermittent idle problems sometimes is cracked rubber intake air tube connectors. Those can be tough to find/troubleshoot sometimes.

'97 4Runner, '06 F350, '86 4Runner, '05 WR450
http://home.4x4wire.com/erik