I'm going to start this off with a disclaimer. This mod will violate the motor vehicle code in many states that says that a maximum of 4 lamps can be lit (Michigan is one of them) at any one time. With this mod, when the high beams are activated, the 4 head lamps and the 2 fog lamps will be lit for total of 6, which could cause you to be stopped, and written a citation by the police. That is the reason the fogs are normally turned off with high beam activation. Use this procedure (or any of the various options) at your own risk. Neither me, nor anyone associated with this site accept any responsibility for you using this procedure.
The external relay and wires needed for this do not have to be heavy duty as they will not carry the current for the lamps. All that they will do is provide a ground path for the fog lamp relay that is removed when the high beams are turned on.
The following picture shows which relays' terminals will be used for this. The lower right is the high beam relay, and the upper center is for the fog lights.
Remove the two relays shown above. Use the picture below for how to install the relay. I've shown where the wires will need to be attached, rather than relay connection numbers, as those vary depending on which way the relay is installed into the socket. Be certain to make your wires long enough to reach to where you decide to install the external relay.
Wrap one wire around the leg of the relay for the high beams that will correspond to point A on the picture. Attach the other end of that wire to the connection on the external relay that goes to one end of the coil.
Wrap another wire around the fog lamp relay leg that will be inserted into point B on the picture. Attach the other end of that wire to a connection on the external relay that corresponds with the switched section.
The two remaining connections on the external relay attach to ground. For the testing, I used the bolt for the alternator bracket as a grounding point.
Doing this will make the fog lights stay on when the high beams are activated, and automatically turn on anytime the high beams are on. The fog lights can be turned on and off with the regular fog lamp switch with the low beams or DRL. If you want the ability to shut off the fog lights when the high beams are on, or to switch this mod on and off, cut the ground wire at point C, and install a switch. If you want the fog lamps to be lit anytime the key is turned to run, connect a wire from point B to ground.