Thanks for the help. It makes sense, but I went and looked at it and my engine isn't hooked up that way for some reason. There is only one wire coming from the negative side of the coil over to where the condenser and points are. There is one end from both the condenser and points that need to go somewhere. I attached pictures of the way things are, hopefully it'll give a little more insight.
On the left is the lead from the points. On the right is the lead coming from the negative of the coil. In the next picture, I'm holding the old condenser up roughly where it was bolted onto the engine cover with a holding bracket. (An identical one came with the new condenser)
Thanks for the help!