This is the pressure switch that plugs into the transfer case which displays the green 4WD light on the dash. Dumb design; I’m sure these wires break often. I know this part is available from the usual places, but I want to take a crack at repairing mine. Does anyone know what that material is poured around the wires in the sensor? Can I heat and melt it out or should I drill it or what?

I think it is some sort of epoxy. I don't think you'll be able to melt it out. From the people I have heard that have tried to fix ones with broken wires, they have drilled/dug out the epoxy from around the wires and I think they said the wires are attached/soldered to metal strips. Then they just solder wires into the metal strips and seal everything up with some 2 part epoxy.

Shoot! I should have updated...

It is some sort of epoxy or pot plastic. I tried drilling it out and ended up destroying the wires. Then I tried melting it out and I got the torch way too close; I melted the housing.

Luckily I had a second broken one, and I heated it with the torch again, but much slower. I was able to dig it all out. As mentioned, the wires are soldered onto posts, so I re-did that and filled it in with silicon (rather than epoxy). The silicon will allow the wires to move without breaking like an epoxy might. Plugged it in and it works.