Most ordinary fog lamps really aren't useful this way. There are vehicles that operate one fog lamp or the other to provide a cornering lamp function, but they have specially-designed fog lamps with an extremely wide lateral light throw to the outboard side (the right fog lamp throws very wide to the right, the left lamp very wide to the left). Most fog lamps, as such, are
useless in their own right, though, so depending on whether and how yours are horizontally aimable, perhaps you can aim them outward to mimic this effect. Then disconnect the existing fog lamp wiring and use these lamps only for the cornering function.
As for the control circuitry: Most US- and Japan-market factory cornering lamps light when you put on the turn signal, and remain lit until a couple of seconds after the turn signal is cancelled. If you want to wire up add-on cornering lights so they work this same way, there's a ready-built control box you can buy. It's called a "delay on release relay", made by Amperite, and is their part number 12D2SST1; a quick Google search shows they are a little difficult to buy because nobody seems to have them in stock, but they aren't listed as "unavailable", you just have to wait (such as
here). If you want to be able to adjust the delay time from 1 to 10 seconds, the part number for that control box is 12D1-10SSTB, which looks to be a little
more readily available. Or,
this diagram would seem to be a brew-it-yourself approach to the same idea.
The only tricky part I can think of would be wiring it up so the cornering lights
don't come on when you use the hazard flashers, only when you use the turn signals. I guess on some vehicles you could tap into the hazard flasher switch and put an inhibitor relay in the delay-release relay's trigger circuit.
