I suggest making this "Full Screen" to see the video better. Problem with fuel dripping through main metering system into venturi after vehicle is shut off. Watch for a few drips coming from bottom of horizontal bar near bottom of throat. Engine has just been shut off. NOTE: This is the wrong carburetor for this vehicle but this change is VERY common. The '36 Dodge should have a Stromberg EXV-2.
Carter BBR 1 Carburetor on 36 Dodge :: Carter BBR-1 Carburetor - fuel drip after shutoff video by 1936 D2 - Photobucket
See also this discussion on modern fuel problems: Is Modern Gasoline Incompatible With Carburetors? Please Help!