does anyone know where this piece goes in a 1924 touring? Its 39 3/4" long 5 5/8" wide 3/4" thick and has a dado the full length on on side

Douglas, I went out and measured the back seat floor boards on my 19 Touring and they are only 35 inches long and certainly not original to the car but the hinged lid built under the back seat, also not original, is close to your measurements. Like I said my 19 Touring was adapted over the years by the original owner so I really do not know what the rear floor boards look like and if the set up under my back seat was a home made "option".