That accessory connection is always hot, key on or off. You could use that connection and run it through a relay, with the coil tapped into the running light circuit.

 

always hot accessory leads are not switched key on, so your fog lights will need a separate on/off switch

 

why not get some LED fog lights, the LED's would draw low current and then you could splice the LED fog light wires into your headlight bucket headlight wires