I know you have stated that this noise is coming from under the hood… But my 1st educated guess is that it is indeed coming from the front wheels…and just sounds like its under the hood…Your wheels are located under the hood in some respects so…its a close call.
Anyway when you apply your brake lightly as you described Your front brake pads have more of a tendency to “chatter” this is when the pads move or occilate within the brake calipers…producing a groaning sound. The solution …IF IT IS THIS>… Is to put some Pad Quiet on the BACK of the brake pads. I personally use Permatex " Ultra Black " which is high temp gasket maker… It is much thicker than the brand name Pad Quiet products… and works PHENOMINALLY to quiet pads…
My other educated guess is that your front rotors are “GLAZED” which happens over time…the rotors get polished and coated with random dirt/road grime/oils etc… and when this occurs…the pads can really get noisy…almost like a wet finger on the lip of a Wine Glass…its sort of the same phenomenon occurring here… The solution is to take some medium grit Emory cloth to the rotors to Roughen them up…basically sanding the rotors to roughen them… this will make the pads bite into the scratches and actually improve braking performance…
My LAST educated guess is that your Power Brake Booster has a leak in the Diaphragm and what you hear is a sort of whistle thru this perforation in the diaphragm.
Now ALL of these “guesses” can actually give you the symptoms you are experiencing…so they are all valid… The least likely is the brake booster…because you would notice its more difficult to stop…and or it is not “power assisting” your foot on the brake pedal… I think you would feel it…it would feel more like putting on your brakes while the engine is NOT running…and trying to stop the car.
I would attack this in the order I listed… See what you get… I bet its a combo of choices 1 and 2 and neither can hurt your situation. LET US KNOW
*** Re-reading my own post… I will let you in on a little secret…my money is on CHOICE NUMBER 2 “GLAZED ROTORS” making the rotor “SING” actually… ***