Self amalgamating tape is widely used in the telecoms industry, amongst others, we use it to seal connectors, repair damaged cables, etc. Over a short period of time it bonds to itself and you can't simply unwrap it (if applied properly), it has to be cut off. I've used it on antenna cables and connectors on deep sea ships, and more recently on production platforms out at sea. I have yet to open a sealed joint or connector, several years after applying the tape, that has let in water (and I'm not likely to now I've retired!

).
As you apply the tape stretch it until it is about half it's normal width (or to just before it snaps) and then wrap the damaged area, overlapping by about 50% (if the tape isn't stretched it won't stick to itself properly). Wrap the tape to about an inch either side of the damage, wrap it one way then back on itself, i.e. two layers, any more and it will be too thick and look unsightly.
Bob