Oh gee. Mom went to assisted living so I have pre-inherited the jag s type. It has 32k miles always garaged and maintained. Car bought mom by dad 2 months before he passes in late 1999. It sat for three years, new battery, started fine. Drove great 60 miles to my home. Now rough idle and marker lights and tag light out. Changed fuses and bulbs to no avail. She wants me to keep it, but seems I can’t win. Please any ideas on this weird issue would be great. My husband is about to send me off the Blue Ridge Parkway in the car 
Welcome, Lisa. Wow, only 32k miles? Mine has 225K. That’s a very nice gift, and I remember once driving on the Blue Ridge Parkway, beautiful scenery. Its on one of our 25 cent coins.
You have found the right place to ask such questions.
First, lift up the trunk floor and see if there is water down there under the spare tire, and soak it up. It sometimes gets in around the tail lights.
Is there a wire dangling in the water around the right tail light. If so, pull it up and secure it with tape or a zip tie or something non-conductive.
Which marker lights, front or rear?
The marker lights and license plate light are powered through relays located in the trunk fuse box. They look like a little cube with 4 or 5 spade tabs. They are a common item at any auto parts store and easily replaced.
There are 3 fuse boxes, under the hood, behind the passenger’s kick panel, and in the trunk. Check all the fuses there.
Rough idle could be a lot of things. Is the check engine light on? You might go to an auto parts store and ask them to read the trouble codes. They usually do this for free because they want you to buy what you need there, and you can even buy a code reader if you want. I keep one in each of my OBD cars all the time.
Let us know what you find.
Rough idle could also be caused by three year old gas or water in the gas. The gas tank is under the back seat on both sides of the driveshaft. I think there is a drain plug, or you might siphon it out or run it until it is empty and refill with new gas.