The light switch does directly not recognize a key. However, a bad ignition switch can lead to problems w/ lights. Since you are not reporting issues like radio stuck on or key chime continuing after removal let's assume your ignition switch is fine for the moment.
Also, to eliminate the obvious..... when you say on, you not only have the ignition on, but the engine
is running correct? On my '99, the lows - fogs and high beams will only illuminate with the engine running. They will not when the ignition is on only. The parking lights will illuminate w/ ignition off or on and w/ or w/o key in ignition. For example - if you had the headlights on and stalled the engine, the lows/fogs/highs would shut off and only the parking and city lights* would remain on. The high beam flash (pulling stalk towards driver also works regardless of ignition position or if there is a key in ignition.
*city light is a small (5W bulb IIRC) located in the low beams housing which can be confused for a dim low beam bulb.
Anyhow, if you motor is running and you're not getting headlights, the problem could be a # of things: bad ignition switch (ruled out per above but not 100%), bad light switch, burnt out bulbs, blown fuses or incorrectly seated headlight housings. Since you get the flash to pass (high beam flash w/ stalk pulled towards driver), let's assume headlight housings are seated correctly, fuses for high beams are fine as are the high beams bulbs.
Now we're down to a couple of things.... light switch, bulbs for fogs & low beams and fuses for each. Easiest to test quickly are the fuses. There is a diagram inside the fuse box so reference yours specifically but generally the fuses are:
Row & # Description
A1 --- High beam right (should be fine since you get flash to pass)
A2 --- High beam Left (should be fine since you get flash to pass)
A7 --- Fog Lights
A9 --- Low beam right
A10 -- Low beam left
Test the lights after swapping and if the issue prevails, you should move on to the bulbs.....
Pull one of the headlight pods (instructions in your manual and tool behind spare tire in tool-kit or you can use a 5mm nutdriver or small socket. Once the headlight pod is out, remove the back cover and swap the hi-beam (we know it works from the flash to pass) w/ either the fog or low beam (they all use the same bulb - H7 / 55W). Incidentally, the placement of the bulbs themselves in the headlight pod is counterintuitive. The low beams are in the upper slot while the high beams are in the lower. Re-insert pod and test low, fog, highs and flash to pass again. If one of them that did not work before now works and the one that did doesn't it's a bulb issue. Go get replacement H7 bulbs (for both sides) and replace all that are needed.
If the issue still prevails, it most likely is the switch itself. It's easy enough to replace - directions and p/n are available using the search function.
Report back your findings....even if they are "opps I didn't have the engine running" as it will help others.
