I looked for prior post specific for "sticky paddle shifters" but found none. Anyway, mine have been that way for almost two years but was I was fearful to fix. I also have a jeep YJ where there is also a known problem with airbag cover becoming sticky. From Wrangler blogs, one owner cleaned off the residue with denatured alcohol. Took a little elbow grease but the process was very successful. So I attempted the same with the Jag paddles. First removed them then wiped repeatedly until all the tacky glue like substance was removed. It did not take away any of the color but left a tach free paddle. Time will tell if it is only temporary.

 

Nice, I took mine to the dealer and they replaced them as well as the starter button that was also sticky and fading.