My girlfriends 93 mazda mx-3 doesn't start sometimes and leaves her stranded all over the place.
It always starts fine cold, but for example she went to get groceries the other day, came back out and it wouldn't start. After waiting for about 10 minutes it started fine again.
The only way to get it to start when that happens seems to be leave it and wait 10 minutes, if you keep trying to start it it doesn't work.
It sounds like it wants to start just doesn't fire up, so I don't think it has anything to do with the battery or starter. She still has all the interior lights and headlights aren't dimmed at all.
And sometimes it idles high around 2000-2500 rpm not sure if the problems are related.
I was thinking maybe the fuel pump, but it's usually fine and never stalls while running.
Any other ideas?
She has a brand new distributor and wires too.

Replace the Ignition Control Module (ICM), which is super simple to do on that car.

She got the whole distributor like a year ago, not just cap and wires, shouldn't the ICM still be fine?
Is there anyway to test it before buying a new one?

The ICM, I believe, is external to the distributor on that car.

Do you know where it would be? I've tried looking on the internet but all it says is in the distributor.