That's what it sounds like to me.
Anyway, my 95' injected YJ is a bear to start when it's cold. Like below 35f. I have to turn the ignition (not the starter) on, and wait. And wait... until I hear, under the hood, this clicking noise. It's coming from one of the relays in the box in front of the battery I've discovered. So, I sit with the ignition on and after a while the clicking starts, and then the check engine and up shift light blink in time with the clicking. when the clicking stops, and the engine, upshift lights are on solid I can turn the key further and it will fire. If I try to start it before waiting for all that nonsense to happen, it just cranks over, and over.......................
In the warm weather it's fine. fires right up. the colder it is, the longer until the clicking starts.
So, I'm guessing (My shop manual is useless here) one of those in front of the battery is the pump relay, and it's going south.