clearly it's the rad fan switch (the one in the radiator itself) as you've bridged the wiring to it and everything else works. replace it and everything else will be fine, but it's worth replacing the whole wiring, relay and fuse as they were inadequate from the factory as mentioned

the temp sender in the head (exhaust side) is only for the gauge (nothing to do with the fans or the ecu)

the blue temp sensor underneath the inlet manifold at the back is only for the ecu (cold start fuelling etc), again nothing to do with the fans or the temp gauge