Only the deluxe passenger car models were equipped with wood-grained dash panels and garnish mouldings. The standard models, including your sport coupe, were originally equipped with "interior gray" (more brown than gray) painted panels.
The grain pattern used was changed during the model year. Early deluxe phaetons and roadsters dashes were straight grain. Mid-year and later deluxe versions of those two body types' dashes were burl grain.
Early deluxe Fordor and Tudor sedan, cabriolet, convertible sedan, and Victoria dashes had a burl grain upper section (surrounding the attachment points) and a straight grain lower section. Mid-year and later dashes in those five deluxe body types were all burl grain. The garnish mouldings had straight grain throughout the model year.
The deluxe coupe wood grain was unique. Initially, the dash and glove box door were all burl grain. That was subsequently changed so that while the glove box door, the counterpart raised panel on the other side of the dash, the raised panel surrounding the instrument panel, and the upper section were still done in burl grain, the background area surrounding the raised panel around the opening for the instrument panel, the glove box, and its counterpart raised panel was done in straight grain. The raised portion of the lower horizontal section of the door garnish mouldings was done in burl grain and remainder in straight grain, as was the rear window moulding.
The photos below are of an early deluxe closed car dash and the later closed car dash from very low mileage cars with their original wood graining pretty well intact. Also shown is the original base color from the back side of the dash in the second photo.