Ran into the same problem with an old S/S on my current flat stick, they do tend to degrade after awhile.

Found this silicon fusion tape at the local True Value....we used something very similar for wiring harnesses on
commercial planes when I worked at Douglas Aircraft many moons ago. It only adheres to itself, but it last a long
time and gives a good/clean slightly tacky finish to whatever you apply it too.

Just do a 50% overlap and a slight stretch of the tape and cut the clear film away as you go.

Also if you want different colors, there's many to choose from on Amazon.