So I took the trim piece off again yesterday and discovered my problem....
When I first disconected the wires, I thought that would cut off the power to everything but I was still getting the trunk popping open. It turns out that because the connector coming from the trunk (that attaches to the connector on the trim piece) was so corroded, the water was still getting in the trunk and it was shorting out the trunk latch. I verified this by cutting the connector off and touching a couple of the wires together. Sure enough, it would pop the trunk latch. I have taped up the wires tightly and will have to order a new trim piece, as well as a connector for the wires that attach to it.