I just finished programming my 2 remotes on a '99 XJR.
I found the thread and FAQ results and tried and tried to get the remotes to link. The only button on the remotes to work was the alarm. (wife was not happy about alarm going off in the garage at 7am)

So I stripped down the remotes and found that oily residue and general gunk was on the circuit board.Remote board.jpg

I cleaned it with circuit cleaner and a lint free cloth, re assembled the remotes.
Followed the reprogramming instructions, and both remotes now work.

I did note that the reprogramming instructions missed a couple of important details.
1. Insert ignition key into the ignition switch barrel, but do not turn it..
2. Hold the turn signal switch stalk in the "flash to pass" position and turn the ignition on with the key(to position 1) (while holding the turn signal switch in "flash to pass").
3. Then repeatedly flash the lights with the turn signal stalk until a confirmation chirp is heard (usually five or six flashes). four flashes
4. After hearing the chirp, depress the each button on the remote transmitter being programmed. If the remote was accepted, there will be another confirmation chirp.
Make sure you have all remotes with you and do all of them at the same time
5. Turn off the ignition and test the remote.

I highlighted the additions I had to make in bold for reference.
So if your remotes don't work, try cleaning the circuit boards.