I own a TT truck that was bought new in 1924. It came with hood, front fenders, TT running board and a firewall. Seat, cab and bed were left up to the buyer to install.
My Dad and his brothers were the buyers and they just added a bed and a seat. The truck was used to replace the horses and wagon in a cotton gin operation. I guess they were used to an open wagon so they never did add a cab.
Much later a 1932 BB truck was bought to replace the TT. I have it also. (it has a cab)