Jiggling the shifter doesn't bring the backup lights on ... so, it doesn't appear to be the bushings.

Checked the electrical plug on the transmission ... it is cracked wide open, and filled with grease. I doused it with electrical cleaner, but the backup lights still don't work.

Any opinions on whether I should replace the electrical plug to the transmission? If yes, can the plug be bought separately and spliced into the existing wiring easily?

Thanks in advance