It is very common that the rear turn signals end up broken at the rubber area. The usual quick fix is splint it with something then wrap the hell out of it with electrical tape.
My savage was just such a bike with wrapped rear turn signals, I decided to do something about it.
I had an old bicycle laying around so I took of the handlebars and cut two pieces off of them each about two to three inches long. These ended up being the replacement for the broken rubber area.
Now, the rubber area that was broken, I stripped all the rubber I could off of the piece that slides into the fender rail. After this was cleaned the best I could, noticed that the piece had a lip on it, this was ground down a little as close even with the rest of the outside diameter as I could.
Then I drove the piece of turn signal shaft into the piece of handle bar as far as I could but still have the screw hole where it matched up with the fender rail. Then I hammered around the end to crimp it on.
The turn signal itself was slightly egg shaped on the shaft part,so I hammered the other end of the handlebar piece untill it too was eggshaped. This slipped inside the turn signal itself. I had to drill a small hole to line up with the screw hole on the signal where it attached to the original shaft. I also had to shave down the inside of the signal shaft area where the screw hole was so the bar would fit.
Slid wires through bar and fender rail, secured bar to rail with original screw, and drove small screw through the hole I drilled through signal and bar.
Put everything back together and I no longer have turn signals wrapped in e-tape.
The red circle shows the handlebar piece and turn signal all put together. (sorry about picture quality)