Replacing damaged #2 lighting coil

I've replaced the obvous leads and now need to determine where the three leads coming out of the new coil (long red, short Red, Black go.

Need help understanding where long red, short red, black leads coming out of new #2 coil go since old dont seem to have discernable colors and there are two reds.  My thought is that short red goes to white output since it is too short to go anywhere else, but that's a big assumption

Any help very much appreciated, thank you for responding

Martin