2000 Honda Civic radiator cooling fan

Engine Cooling problem
2000 Honda Civic 4 cyl Automatic 150000 miles

My Honda will run hot after sitting in traffic, I notice the fan to the radiator wont turn on, although the one to the ac works. I ran a wire from battery to fan wire directly and fan works. I switched the relay with condensor relay since both are the same and both work for the a/c fan but not cooling fan. I took a meter and tested the socket for ac relay and it read 12v, but the cooling fan socket didnt read, could the be a wire shortage, what would be the next step