The top wire was abit crusty close to the terminal, but was ok after the first inch. But it was getting hot when using ancillaries (Full Beam etc)

I've done as the other guys have suggested and replace the three tail wires.

But the one I'm concerned about is the top one. (The burned one) I don't want to run it without a fuse just incase I have a problem (Dont' want the loom going up in flames) everyone tells me that this wire always gets hot, but I don't want to take any chances.

Just not sure what ampage fuse to run on the cable. And of course trying to find out what it supplies.