Car hiccups bunny hops and stalls and almost dies

Hello everyone
my 95 aj16 xjs is acting up.
it starts hiccups after it gets warm to the point that bunny hops .
it did that on interstate going 65 miles per hour , it scared the hell out of me.
it acts ok when i let it sit.
engine light comes on and goes off immediately when it acts up.
i changed the crank sensor it did not help.
I do not think it is a bad coil/coils as i know the way it acts when it has a bad coil.
i am leaning toward a bad fuel pump , would a bad fuel pump act up all the time though.
any help would be appreciated.

When you say bunny hops, do you mean surges or lurches?
Does it do it at any speed (or RPM) after it warms up?
Did you put a scan tool on it to see what codes might be saved?
If no codes, have you tried driving around with the scan tool plugged in to see if you can capture a code?
Sounds fuel related. put a fuel pressure gauge on incoming line to measure the pressure? I did a quick search for what it should be, and didn’t find anything. I know the 5.3 & XK6 are 36psi. I would think the AJ6 would be more. Just a guess.

Coils are pretty easy to bench test.
I had a similar issue with my XJR. in my instance the cowling rubbed through wiring harness, and the wires where intermittently shorting. That’s what I get for having the dealer work on my car. never again.

it won’t capture any code , i am going to try your suggestion and drive it with code reader attached.