The Borg Warner overdrive essentially works the same, regardless of what it is in. The T handle on the dash only operated the lockout for the freewheel. The solenoid is powered up whenever the ignition switch is on. When the handle is pulled out, the freewheeling clutch is locked, and it also slided a blocker that prevents the solenoid from engaging the overdrive gearset. In thsi position, it drives just as a standard 3 speed would.
Pushing the handle in unlocks the freewheeling clutch, which is nothing more than a one way roller clutch. It also shifts the blocker out of the way of the solenoid pawl. At speeds under 28 mph, you have freewheel action when you let off the throttle (no compression braking_ which allows for easy coating off throttle (saving feul) and also allows for clutchless shifting from second to third. Once you get over 28 mph, the governor grounds out, which allows the solenoid to engage. It doesn't drop into overdrive right away, there's a blocker ring that prevents that. You have to let off the throttle, which allows the blocker ring and overdrive componets to properly synchronize together. Once the overdrive pawl has locked in, you have overdrive. You also have compression braking, as the overdrive locks the freewheel clutch when the solenoid is engaged.
Here's the operation description from the '55 Truck manual.
