I had the exact same thing happen to my 2011 WRX and I just rubbed the disintegrating rubber off and left it alone and it worked fine without a rubber cover.

 

call your dealer and ask the parts department what the part number s for the liftgate release switch
2010-13 are different than 2014

 

I used a piece of rubber sealing tape over the existing rubber that had a tear. If water is allowed to get in for long enough, the switch may go bad.

 

Sounds like a job for Gorilla Tape. Impressive stuff.

 

Thanks for the feedback. I used a piece of electric tape for now. BTW, I added a trunk release button on the inside and will post in his forum.