You might have better luck finding a junker to pull the connector from, it can be tricky to find the housings like these. An easy fix though is like what I had to do for the wire to the blower motor in mine, simply cut the wire at the connector on each side and splice them together (might need some extra wire to make it reach). If you want you can use a bullet connector so that you can still unhook it later, but it's not something that happens often so simply splicing it is likely fine.
