Buzzing Sound Coming From right side of dash

Bad flasher

Under the left side of your back seat is a fuse / relay box . When you first turn the key on the fuel pump relay turns on for a few seconds to prime the fuel system . That relay is in that fuse / relay box ,that is what your hearing . Does the vehicle start an run good , no problems other then the buzzing sound .The vehicle battery is also under the rear seat on the right side . How To Locate and disconnect Battery Buick Lesabre Pontiac Bonneville 00...

remove the air filter and carefully run the engine to locate the source. check the hoses in particular.

Could be seat belt Buzzer / Door / Tailgate not closed securely warning Buzzer Stuck ON since car in park these buzzers do not activate but you said under movement sound occurs .. Mechanically I would Check Altenator for Proper Charge output - Then Ground wires for Battery / Corrosion needs cleaning ?? - Plus Dash Cluster must be Grounded Tightly .

sounds like the wheels are out of balance, is there a slight vibration through the steering wheel at this speed? and does the problem stop if you go faster (please drive carefully)

There can't be any noise after 5 minutes. There are capacitors that take a few minutes to drain down. It could be your clock winding or your abs cycling. Listen and see if it's coming from your fuse box a relay

It sounds like your flasher Its blue and looks like a relay remove your fuse cover and all the way to the right

SOUNDS LIKE A RELAY.CHECK UNER DASH AND OUTSIDE UNDERHOOD.











TIM

check brake fluid level.

master cylinder might be of interest, but i would check the fluid level first

Re:- the buzzing behind the dash:-
Its tiny a fan which carries on running in humid conditions to circulate the air so you dont get blasted by warm air when you use your climate control.It circulates air across the humidity sensor. It keeps running for a while after you switch off, and starts again when you open a door. It does this so that there is less delay in getting the climate control to the right setting when you switch on (or restart).