Sounds like you've got the SM318/Borg-warner overdrive. good trannies, I have one in mine. They're not too hard to overhaul, I'd suggest looking at a '55 manual, as it has a full section on this trans.
To answer the question about the cable and solenoid- the solenoid actually operates the o/d, engaging the planetary gearset that give the overdrive ratio. The cable operates the overrunning clutch, locking it out when the o/d isn't being used. Since you don't have the original cable, I'd suggest the you get a cable for a pto. They're a little pricey, I paid about $40, but they're much better for that application than a standard cable.
