hi, the temperate sensor wire comes off the wiring loom that runs to the right of your cylinder head, that black plug hanging down(at the front) will be the reverse light switch that goes on the front of the gearbox,that is the same wiring your temp wire come off so if you follow it up from that plug hanging you should find the broken wire,get that sorted first,then you will be able to see how hot its getting,fan should kick in somewhere between half way and 3/4.
me personally i wouldnt hard wire the fan so it runs all the time,id rather trace the fault and fix it properly it will be something easy trust me. is the fan switch plugged in on the thermostat housing? located on the right of the head?if yes then first thing i would do is pull the plug off and cross the connections with a piece of wire (ignition must be ON for this) if the fan runs its a faulty switch.but obviously you need to run it up first and see how hot its getting,hence fix the temp gauge first.
hope this helps..

jason.