I am not knowledgeable on the fuel gauge system, but the sender is easily accessed in your car, behind the spare tire, and might be the best place to start troubleshooting…
I’d advise you to search this forum for previous posts about fuel gauge issues.
For example: [xj-s] fuel gauge problem - #3 by gregory_wilkinson-ri …reply by gregory wilkinson describes some simple tests to determine if the sender is operating properly.