My kids love their toys. And sometimes they love them a little too much. In this case a finger on the end of a stick. After trying various glues and tapes, I decided to build a cylinder that is the exact size of the inner dimensions of the original tube, to act as a repair patch.

Slight problem: cheap toys aren't made to tight specs. The tube's inner dimensions varied from 12.5mm to 12.9 mm. So what does one do in this situation? I decided to make a fuzzy tube:

A solid core covers only half the radius, and then I overshoot slightly with a thin (in this case half-nozzle width) set of fins. The fins are just long enough to have a little play. The net result is that crushing the repair plug into the broken ends of the tube creates a snug fit:

I have added an openScad file if you want to make one yourself: