JEEP WONT START

Test ignition module, crank sensor, test fuel pressure with gauge, check compression may have jumped timing belt.

What make vehicle ? year an model too ! Before you replaced those parts did you check for battery supply voltage an check the ground for those components ? You need to get a wiring diagram an see what get's voltage an what is ground ! An see what all is involved , crankshaft position sensor , ECM / PCM -engine computer etc...! Then you need a DVOM - digital volt ohm meter to test ! Your looking for a quick fix an doesn't work like that !

I just have one suggestion, after what all your mechanic already did. I would want to know the fuel pressure reading WHEN IT WON'T START. So you would need a fuel pressure gauge handy, for that time it won't start. Hook up the gauge and turn the key on- if at 59 psi, when the engine won't start, then you know the fuel pump and the relay sensor is not the problem. And so probably not a fuel problem, although you haven't checked the injector circuit, but likely that wouldn't exhibit a problem as you have.
So if not a fuel problem, check for spark when it won't start. Maybe the problem is in the ignition system. Buy a spark tester from a parts store, use it when the **** engine won't start- simple and easy check of your ignition system.

Check fuses first, but could be needs new CPU

The click...click sound is telling you the battery is close to dead or the wires are corroded on the posts. I would put a new battery in and see if that solves your problem or go to a store like Auto-Zone and have them check out your battery and alternator. They also can read your on-board computer which may point you to something else that has failed.

have you checked the crank position sensor? when this baby goes the engine will start and run for one or two seconds then die like its out of gas.

Also the ignition switch may be suspect.

Are you the only driver for this vehicle?
Next time when you refill up,DO NOT TOP OFF THE GAS.
When the gas pump stop,just let it stop. DO NOT TRY to put more into the take.
When topping off,the fuel sensing float is push BEYOND it limit. It will create a short on the wiring to the gauage.
Please ran few tank WITHOUT TOPPING off and see does the flow return to normal and not creating a short.
The fuel pump and gas level sensor is in the same unit. It's costly to pull the gas tank down and replace it.

check the fuel pump

My first thought would be that there is a short in the system dealing with the guage itself.

Eshel

replace the crankshaft position sensor