Back to the first question: It looks like a 242, but it lights-up "part-time" on the dash....is it a 242, and how can you tell?
XJs come with either the 231 or the 242 case. The 242 was used almost exclusively on the higher trim level units like the Limited, while the 231 was used on all the others, and on ALL manual transmission XJs. If you have a lower trim level XJ, then it's most likely a 231 case.
They look pretty much the same, and you don't want to crawl under there anyway, do you?
the shift pattern for a 242 is: 2-F-P-N-L
the shift pattern for a 231 is: 2---P-N-L
On the 242, there will be two distinct detents between 2 and N, but only one on the 231. On the 242, the F position engages when the lever is only about an inch above the 2 position. If you feel a detent at about that position, but no light shows-up on the dash, then maybe you have a 242 and a dead light bulb. Not likely, but worth checking.
If you have a 231 and just can't live without a 242, sell your XJ and buy one that already has a 242 - it's a waste of time to change one for the other if the one in the truck is working...and it's too darn easy to sell one and buy another...and another... Just check my driveway.