1997 Acura TL Left Headlight daytime and bright light does n

Electrical problem
1997 Acura TL V6 Front Wheel Drive Automatic 115000 miles

When I start the engine, a high pitched signing noise comes from the area below the glove box. At this point the left side daytime light does not come on. (Right side is on) If I turn the lights on, the high pitched noise goes away and both headlights work. If I switch to bright lights the left side bright light does not work.
I changed the light bulb but this did not rectify the problem. I also cleaned the 3 prong plug that plugs into the light bulb but still no luck. Please advise on how I can rectify this problem. Thanks.