Fog light help, PLEASE.

[Charlie Guthrie]

Now you have given a hint.(relay buzzing)  The likely problem is that the
hot wire from the relay to the lamp is grounded. The reason the relay hums
is that the relay pulls in but that connects the battery voltage to ground,
causing the voltage in that circuit to drop, causing the relay to
momentarily drop out, breaking the short, the voltage comes back up, and the
relay pulls back in, for as long as the switch is on....until the relay
contacts finally burn up (not very long, usually).
Check your wiring with the bulb removed.  You may even want to remove the
bulb and try switching on. If the relay only buzzes with both bulbs in place
you may be drawing too much power. The bulb has almost zero resistance until
it heats up. The other thing that could be possible is that you have used a
STOCK relay with high power lamps (which draw a lot more current...just like
shorting the circuit).
If this wasn't perfectly clear :-), send me a post and I may be able to talk
you through it.
Charlie Guthrie