[oil pan 4]

Good move, I have been on the Honda forums and can be about as intelligent as the gasbuddy.com forum or a middle school lunch table.

On vehicles I have done LED conversions I run lower amp fuses, I figure that since the LED draws so little power compared to the old style light bulb if there is a wiring fault with the standard lights load removed it could burn up the wire before it pops the fuse.

I have no idea what could be going on there in the dash of your car. The only thing I can possibly imagine is that maybe your vehicle is doing what it is supposed to be doing and you have some kind of "head light out alarm" going off due to lack of current draw.
Verify this by replacing the LEDs with the proper head light lamps, drive around make sure this buzzing is gone. Then try removing one or both head lights and turning the switch on, see if the buzzing returns. If the buzzing returns with one or no OEM head lights installed and when ever you have the LEDs in then you will need to run a ballast resistor so the circuit will draw the same amount of power as standard head lights with the LEDs installed.

Or open up the dash, find the buzzer, remove it if possible then smash it with a hammer (just out of spite).

If one less head light or both head lights being removed can not reproduce the noise then you may have stumbled upon some weird DC harmonics phenomenon.
At that point just by pass the offending system.
Take the factory low beam head light harness and slave it to power a relay, then wire your LED head lights to run through the relay via a fused wire coming off the battery or alternator. A 5 amp fuse will be more than enough to power the LEDs. Then fuse the factory low beam circuit with a 2 or 5 amps fuse, since the factory low beam circuit will only be powering a tiny relay at that point.