A Coupla things...
First, when you talk about "cycling 2-3 times", be aware that the WTS light and the GP's are In NO Way connected. Just leave the key ON (for up to 2mins depending on the cold) and they will stay on despite the light going off
Next, if this happens in the Summer, it's not GP related, must be something else. One a 2000, you can actually "see" the CPS working by the Tach needle so, if it rises while cranking it's doing it's job...
Also, do you see White "Smoke" coming from the tailpipe when you're cranking but it's not starting?
So, that leaves us with what? Well, without some monitoring scanner, to see what the sensor values are, it's gonna be hit-or-miss unless you can find some commonality when it does this.
Cold start Only (as opposed to a restart several hours later)?
No Outside Temperature where does it Not do it?
No conditions where it seems to do it more (low on fuel, oil change needed, parked on a hill etc.)?
Intermittent stuff is always a challenge!
Maybe examine both the IPR and ICP sensors. Make sure their plugs both look good, no missing insulation, not full of oil (a failing ICP will leak oil into the connector). You could try to simply unplug the ICP next time it happens, it will set a default value for the IPR to run on and that would tell you there could be something wrong with it. You can make sure the "tin nut" that holds the solenoid coil on the IPR was tight or hadn't vibrated off. Maybe "rap" on the IPR itself with a screwdriver handle or something (sometimes you can dislodge a stuck pintle inside).
BUT, in the end, what you Really need to point you in the right direction would be to have the right scanner so you could determine what was "Not doing what it's Supposed to do
" when this is going on
If all else fails, consider getting your hands on an AutoEnginuity scanner!