Sit back, get a coffee, this is gonna be a heavy read.
After installing my relay wiring harness (here), I ran into a problem with my daytime running lights (DRLs). I noticed it when I drove to my train station in the morning and parked. When I turned off my headlights, there was a loud buzzing from under the hood, right where my new relays were.
After a quick check, I discovered that it only happened when my DRLs were on. For those not in Canada, DRLs are required (since 1990) on on vehicles. Basically it's headlights or marker lights on while driving and it's automated. To avoid the extra cost of having another set of lights, auto makers were allowed to use the high beams, at a dim setting, as DRLs.
The method used on the Jeep TJ is called "Pulse Width Modulation" (PWM). In it's simplest form, it basically means that a module turns the high beams on and off really quickly. With a standard headlight, this on off quick action has the effect of not letting the filament reach full brightness, essentially running them at 6v, or half brightness. (I'm really oversimplifying here). When the "On width" is the same as the "Off width", you have a 50% cycle, and 50% voltage (for all intents and purposes).
Normally, this is not noticeable, and to the naked eye, is just looks like a dim light.
Since I added a relay to provide direct battery power to my head lights. When the switch is on, no problem, however, when the DRL module is controlling the high beams for that 50% brightness, the high beam relay is being flipped on and off at a rapid rate, causing the buzzing sound.
Photo via www.justanswer.com