1998 Mazda 626 No running lights

You have one fuse for your side markers, tail lights and dash light, and another fuse for your low beams.

Does the dash light work?

Your low and high beams are off the same bulb. It has dual filaments inside the bulb. I have seen that both low beams burned out.

I would remove the bulbs, one at a time, and test them. Your bulb has 3 prongs. Use jumpers wires, connect two prongs to the battery. If the bulb is good, you will have light in two of the three combination (Prong 1 prong 2, prong 1 prong 3, prong 2 prong 3). If you only have 1 combination, replace the bulb.

I just looked at the wiring diagram. There is a relay under the hood that controls the headlights. Try swapping the relay with something else. I mean another relay that controls your rear defroster, or something.

If swapping relay doesn't work, I have to say that your switch is bad.