Most "old" cars with OD had a 3-speed transmission with a planetary overdrive unit mated to the rear in place of the conventional tailshaft housing. The pic below is of a typical Warner T-85 OD, everything forward of the OD section is the same as the non-OD unit.

These had two controls, a cable operated lever on the side slid the sun gear into position and an electric solenoid that engaged the OD. The throttle has to be eased a bit to allow the OD to engage, so it can't be engaged under power like the Laycock variations.