Well, it could be the sending unit. With the pink wire disconnected, everything except the fuel level meter works perfectly. So, I would try running a fresh, temporary, fused wire to the pink wire connection at the fuel sender unit. Disconnect the existing pink wire at both the dash end and the fuel tank end (just in there's a chaffing fault along it somewhere). Put a five amp fuse on the new fresh wire and run it to the pink terminal at the sender unit and then see if: 1) the fuel level gauge works when the car is on, and for how long, or 2) whether that new fuse blows. If the new fuse works for a while, and then blows, upping the amp value of the fuse might be a possibility to consider... but it is the fuel tank....
