A few years ago on one of our wilderness moose hunts my wife tore a hole in her new hip waders from a screw sticking out of the old freighter canoe we were using.
That night I rummaged around for whatever I could use to patch it well enough to last until the end of the hunt.
I had a couple of jumbo elastics along that I make from old tire tubes (great for all sorts of things), and I cut a circular piece from one of them. I also had a tube of silicon called "shoe goop" or similar name (I just noticed that others have recommended shoe goop too, so my recollection of the name was correct).
I cleaned and roughed up the surface area where I would be applying the silicon and then went ahead with the patching, applying weight on the patch and giving it an entire day to cure.
Years later, the waders are no longer new, but surprisingly, the "temporary" patch is still as solid and as totally waterproof as the day I made it.