It sounds like a bad dimmer switch.
Even with a good headlight switch if the dimmer switch is bad OR disconnected then you will not have head lights. I learned this when changing the ignition last year.
I also have a 88 XJ and recommend if you change the dimmer switch to also change the ignition switch since the same two bolts hold both on. I think the dimmer runs $15 while ignition switch runs $10-$12. I am not talking the lock cylinder on the column, I am talking the ignition switch which is mounted about half way down the column.
To change either switch you will need to remove the two bolts holding the column to dash board. and let the steering column drop. This means the lower trim of the dash is also removed. You will need a set of metric ignition wrenches to do the job. I got my set at Sears. They are just combination wrenches with 2-3 inch handles, perfect for tight places.
Once you install and the new switch make sure it is set so it will dim lights. If you change the ignition switch make sure you get the tilt or non-tilt switch, there is a difference.
One more thing with the age of your XJ I'd throw on a new head light switch. It should run around $15. Have the parts guy show you the release button and go for it! I had my ignition switch fail, changed it and then 10 days later I am 200 miles from home and the head light switch fails. I am changing the switch in the parking lot of a big box chain store in the dark - no fun.
If you plan on changing the one change all 3, it will be smart money. Find a buddy who done an ignition switch before, he will know how to adjust the dimmer switch.
