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For those of you looking to replace the "alien beacon" I finally found a replacement that works! Its from amazon, the Eightwood AM FM car stereo antenna, $16. Here's a picture on the Jag
Those stubby antennas are popular with Miata owners too. Funnily enough, when I started taking apart the amp/cd changer rack in my jag I discovered the original antenna (which still popped up with the radio being turned on) had been replaced with a completely internal one glued to the inside of the back right fender. I'd have to go look at the brand on it, but basically the original antenna was already bypassed but inexplicably, had been left with the fuse in so it still popped up even though it did nothing. Removed the fuse, problem solved. I'll be sure to look up the brand next time I'm in the trunk.
Simple to install. Biggest problem was connecting the antenna. It comes with a short antenna lead - about 8 inches, which has a DIN connector. This does not match the connector on the Jaguar. I am sure there are adapters but without a Radio Shack store I had no idea what to order. I just cut off the lead off the old "alien beacon" and soldered it to the lead from the new antenna. works fine.