If it indeed sounds like the glove box and it goes away when you press on the glove box then you need to insulate the plastic dash cross section that runs under the glove box in front of the knee airbag there are no screws in that 20 inch section of plastic and it buzzes against the steel crash bar. Usually need to pull the glovehicle box to get it insulated w foam tape. Have fixed a dozen or more of them. But based on the fact that you say engine on only. Check heat shields also the one by the turbo and catalytic converter back side. Also one above center muffler aND outer muffler (that one can get cut out and pulled, no purpose) Lastly if it is a really loud buzzing from outside check the lower cat converter bracket, they commonly break or crack. It it near impossible to see the crack. Usually requires a mirror to see the crack. I won't even explain how to replace it, my fingers are tired enough...
Fisker of Cherry Hill