It has been opening just fine for months after being taken out of storage. Today I drove it an got a "Fuel Cap" message on my display.
Got home and was going to check the fuel gap and couldn't get the cap open. Tried the find the manual cable in the trunk.... there wasn't one.
No surprise...I think this car was built after a long holiday. Pulled and tested relay and fuses. Left relay out and installed jumper wires with momentary switch in the trunk.
This works fine for now, but would like to fix it correctly.
Looks like the problem might be in the switch on the dash.
Any suggestions?

 

I just went outside and check this out on our X204. You are right: There is no manual cable. Maybe they mixed it up in the manual with the Ford Fairlane '97. That one has that cable....
Since you did an alternate design now with a momentary switch, which opens the lid, this would suggest that the actuator at the lid is OK. That leave cables, relay and switch in the dashboard. I would suggest to remove the switch from the dashboard, open it and clean the contacts inside.

 

I'll do that. I did bench test the relay.
I think after I solve the problem, I will leave the momentary switch wired in as a backup.
It mounted very nicely and looks good in the trunk. Chrome 16mm low profile.

A YouTuber put out a video showing the manual release in his S-Type, but didn't give his year model.

 

Actually - before taking the switch (from the dash) apart, look at the pins of its connector, clean them, and see, it that makes already a difference.

 

For the manual release cable, I'd peel back the trunk liner in that area and take a peek. I bet somebody previously had the liner removed and didn't route the cable correctly when reinstalled.

On the electrical side, wiring diagrams are here:

JagRepair.com - Jaguar Repair Information Resource

Open your diagram and proceed to figure 12.1 or 12.2. Before doing anything even remotely approaching work, reinstall relay R8 in the trunk. Place your finger on said relay while a helper pushes the button.

If you feel a click, the control side of the circuit is good. This includes the switch, corresponding fuse, and wiring between the switch and relay. It does NOT confirm the relay is actually sending power to the door release solenoid, only that the command has reached the relay.

If no click, check fuse F33 in the primary junction box, inside the cabin just forward of the right front door.

If the fuse is good and still no click, swap in a known-good relay. The fog lamp relay (R11 under the hood) would be a good donor.

If all no help so far and the relay remains clickless, you know the fault is with the control circuit, possibly the switch or wire run.

If the relay has been happily clicking all this time, check fuse F46 in the trunk. This is the actual power source to energize the door release solenoid when the control circuit activates the relay.

 

I was thinking about the push-button, which you installed meanwhile and which you intend to leave there:
I assume you have picked up power directly from the battery in the boot (=trunk).
I hope you also installed an inline fuse! Close to the battery-plus. I would suggest maybe 10A.
Cause if you have not and something goes wrong, this could lead to quite some sparks, even fire - and given all this is in the proximity to the petrol tank and filler: It could also lead to a big "booooom"!