Yes the two lives come from a relay which is located in the fuse box (Yellow one) the rad switch trips the relay (Switched earth) when it closes and hence powering on the fans. Either you have a bad connection at the relay or a break in the live wire to that fan someone along the line.

TBH the fan circuit is sub standard to start with and many have been wired as the fuses etc melt due to the fans staying on for to long etc, you could either do a rewire (Plenty of info and diagrams on here or trace the live for the fan that is not working back to the fuse box and try to repair it, or run another new live back to the fuse box.

As for the overheating is it only happening after sitting stationary (In traffic etc) for a while? If so then the fans not working would cause this, if it's when it's moving then it's not going to be a fan problem!

Another bit of advise if you haven't done so already the fuel pump power also needs checking UNDER load, the wiring degrades over the years and builds up resistance and so the pump cannot draw the power it needs under load and so you can end up with an engine meltdown. Again many have been rewired for this very reason!

Martin