Well, the new coil works fine but the hesitation/stumbling remains.

Recap:
* The XJ starts fine and idles okay; when I accelerate it has increasing stumbling/hesitation from 1500 rpm to 2400 rpm and the tach bounces around wildly and/or goes to zero; at 2500+ rpm there is no hesitation/stumbling and the tach is normal.
* New CPS, TPS, and coil; grounds refreshed; tune-up done.

The hunt continues...

Did coil/ICM come as a unit?

No, just new coil; ICM is original.

Hmmmm. I hate throwing parts at a problem, but there's no good test procedure for the ICM.

I found an ICM at Rock Auto for reasonable $$; will take a few days to get here; local parts stores want $$$; could go salvage yard for way less but I'd rather not have to guess about reliability or useful remaining life of old electronics.

Before I pull the ICM trigger at Rock....
If it turns out to be the ICM, major puzzle solved. But if it's not ICM what would be your next suggestion? Tach gets its input signal from ICM via ECU? ECU bases that tach signal on inputs from ICM? and sensors (which ones? CPS? TPS? CKS?) and what else? I'd like to be sure I've eliminated all the tach-related possibilities on the ECU/ICM input list. I'll do some more homework on ECU/ICM inputs/outputs but would definitely appreciate any expertise you can share.

That sounds like the stumble/hesitation I had on my 87 renix except I don't recall it doing it in park/neutral. The last parts I put on before it was cured was an o2 sensor and a new vacuum harness. I tested/replaced other parts to death before that. I'm not saying your's is that, but if you're ordering from rockauto, you might want to pick up an NTK o2 sensor and maybe a vacuum harness if they aren't too expensive. If you've never replaced them, they are likely old anyways and will need replacement eventually.

I hooked up an analog multimeter to several of the sensors (one at a time) so I could see if any acted erratic when the hesitation occurred. The old o2 sensor seemed to work according to the meter, but it might have been a bit slow on the back and forth voltage. So far my XJ is still working fine 1-2 years later. I hope you figure it out!

ECU controls the ICM. Who knows what's going on inside there......

Dude, ...did you ever measure your fuel pressure, This sounds like a dead ringer for a fuel starved engine. Lots of testing with a fuel gauge you should be doing, like ..it should hop right up to pressure when you turn the key on, it should run within range, and should hold pressure after you shut it off for a set time. This was a first step, forgive me if I missed that you did it but I re read and don't see it.

Later I tried to duplicate what I did with the 3.5 V led's from China, with a bulb out of a $ store light...didn't seem to work...(5V backwards might have cooked it)

ECU to ICM signal test. I guess this wouldn't be much help with an intermittent problem. I didn't try "T"ing off, back-probing. (probably the LED would just ground the signal.

Many thanks for all the replies.

Super -- great ideas; the O2 and vac lines are definitely still on the suspect list; my measured vacuum was 12-13 at a couple of spots where I think it should have been at least 15 to be normal; I've replaced the vac lines at least three times in 25 years, last time 5yrs ago; time before that 8yrs; solved issues both times; maybe time for a new set. The O2 is probably getting long in the tooth; was replaced 70k miles ago but not sure why; probably to pass a smog test, not to fix rough running; but I've definitely read about the O2 being a possibility for rough running; from my original list of possibilities O2, vac lines, ICM, and ECU have not been replaced (yet); TPS, CPS, and coil are all new and scratched off the list of possibilities; did a tune-up, too; so far, no silver bullet.

97g -- spot on, fuel pressure is an issue; originally measured at test port: fp jumps right to 31 at key-on; drops immediately to 26 at idle, 34 w/ vac removed, should be 31/39 so 5psi low at idle; holds pressure very well after key-off; to test the fp regulator I squeezed the fuel rtn line and the pressure went right up; replaced the fpr and remeasured: 31 at key-on, 29/36.5 at idle, still 2psi low; more work needed somewhere betwixt pump and rail <groan>.

DF -- thank you for the video; good production; your engine bay looks great; I like the homebrew test jig; who knows, I may get to the point of looking at the ECU-to-ICM signal (and after that how to decode the flashes -- was that Morse code? Mine's probably sending S-O-S).

Weekend is coming up; that's when I'll have time to get back into it; I'll buy some parts in the mean time; Christmas in July.

10-4...I mostly only did it the once, holding the camera and the jumper. I'd guess why it missed a few beats has to do with how the CPS signals while cranking. Hooked up it would have started at the first flash or so.

The test DOES check not just the CPS, but the wiring to the ECU, ECU function, cranking speed, (must be > 300), and the wires to the ICU. (at least while cranking). No so bad for a 2 minute test you can do with a 5 cent led bulb!

You could pull one plug wire, put it on a spare spark plug, get her goen enough to mess up and see if you have a crisp,sharp blue spark while it's stumbling...

Does this mill have a distributor, if it does, how is the shaft play? Hint, should be none, side to side. Not so familliar with your setup, but how are the injector resistances, or does it have a TB? You mention the CPS, is that the crank sensor or the cam position sensor? Both are mopar only items. JY might be a good stop for some cam sensors just to see.

Thank you, DF. The additional details about your LED ignition test definitely up the value. I also like Plan B with the spark plug and will likely perform that test this weekend. Right after I swap on the new plug wires; new Taylor's arrived today.

Thanks for the ideas, 97g.
Yes, has a distributor; didn't notice excess shaft play when I replaced rotor/cap but I'll double-check this weekend.
This XJ has a TB and injectors; I haven't checked the injectors closely but no obvious signs like fuel on the rail; didn't know about checking the resistance but I'll read up and maybe get to that this weekend.
I mean Crankshaft when I use CPS (and cam shaft would be CKS for me). For the CKS, I've played the head-in-sand card hoping the issue will be solved by something else first. Don't you have to pull the distributor to play with that?

Don't worry about the cam sensor. Renix barely uses it, will run fine with the lower wires on the dizy unplugged. (yea, the crank and cam sensors have too many names in my opinion). The letter salad, doesn't work at all for some of us. (sync pulse generator....?

Well shoot...thought you'd have changed the wires before buying a coil. Fingers crossed.