The taper helps seal the connection. The wire is held in by the male end metal connection. It needs to be able to Snap in place. If its not snapping into the coil female end the male metal end needs to be opened up a bit until it does Snap in and contain itself.

You might need to pull the wire further through the boot so it can extend further into the coil to its snap in position, then slide the boot tight onto the tapered end of the coil.