The epoxy is at the back of the connector, far from the contact points. My main concern is that if I put solder or some other conductive material on and somehow slop it, I will get shorts, not only between the fan connection pins, but between the pins and several other nearby metal spots (I have no clue what they connect to, probably something on the other side of the board).

The fan has four wires. The computer uses these to control the fan's speed, but I have no idea what the actual circuitry or protocol is. I think at least one wire returns some kind of tach signal, since I have software that shows me fan rpm.

I may try to cover these nearby contacts with tape or something before I mess any further. I sure miss the old days when you could do this kind of work without an electron microscope. My hat's off to those who actually design this stuff. To me it actually does seem like sorcery.