Jaguar X-type license plate bulb.
 

Ok so I have an x-type (03) and the idiot that owned ot before me thought that it would be a good Idea To put an led bar over the plate instead of just led light bulbs. It did look decent until It stopped working the other night. I checked the fuse and that's fine so I pulled down the trunk panel and found that the way it was connected shorted out the lights. So I'm trying to put regular bulbs back on so I don't get pulled over but the bulbs that advanced auto gave me don't fit and I checked around and those are supposedly the right bulb but it doesn't work I don't know what to do. it looks like there might be a connector missing but then the bulb wouldn't fit. The spot where the bulbs would go looks like a connector with two prongs please help

The bulb you want should look something like this:



That is the LED version of the bulb you want. You simply push the wedge connector of the bulb in to the prongs. Note that with an LED bulb, it will only work if it's inserted a certain way, so if you push it in and it doesn't illuminate, rotate the base 180 degrees and try again.

Advance auto Auto zone both sell a led bulb that will fit

When I got my car the license plate bulbs were leds, but with no covers, so the leds were badly corroded and had very little light output. I replaced with new leds and made up a paper pattern to fit the recess on the light housing by pressing it to the edges. I then cut out the shape from polycarbonate sheet, with filing and cutting to fit one side. The other side is a mirror image.
The clear covers will protect the led bulbs, and should not need removing for some time. I put a small bead of silicone rtv around the edges of the covers and taped them in place until it cured.
There aren't enough X350/X358 Jaguars here in New Zealand to have a junkyard source of parts near where I live, sadly.