Clean off the tape and attach it with a dab of silicon adhesive. Tape it down with painters' tape for a day and it will be good.
I like the looks of your carbon fiber shifter, but I wish the factory ones were a little heavier. I do like the look of @Soareyes 's shifter. That might be going on my Christmas list!

 

I saw somebody with a similar problem with a 911 shift ****. They pulled the metal/plastic off and glued it back in the video.

 

Maybe this?

 

The trickiest part is the weight, but the video below might help you with that. I went with medium+ weight (the 2nd heaviest). The 'coin' is the top part with the shift pattern. You could get the exact Porsche shift pattern if you wanted to, but you'd have to pay for the 'custom' engraving. Roy told me it's quite involved, since it has rounded edges. Their regular (straight -not slanted) pattern is good enough for me, so I went with that. You can specify different colors for the 'coin', and the 'shaft'. I went with 'silvergray' on both (like on the video), which matches the shifter plaque (718, 911, Carrera, etc), but you can go with black on one or both parts. I also went with smooth nappa black leather, to match my OEM ****. Hope this helps.

 

I would use something like this:
Silicone stays flexible so you won't have issues with it popping loose when the plastic shrinks and expands with the weather. Any brand clear silicone will be fine. You can find it at your local home store, Walmart, or auto parts store, or order it from Amazon.