That is indeed a Truckstell torque tube overdrive transmission. "Tip-toe-matic" si their name for the way it should operate. There is a decent amount of info on the web about it. I would bet that your Suburban truckstell has a number of A-101 on it. The small cable is operated by the clutch and brake rods located in the engine bay. They bring the trans into and out of overdrive while the trans is IN overdrive, which is controlled by the Bigger cable to the rear of the trans. There would have been a decent sized lever by your steering column.
When the column shift lever is placed in reverse, the whole unit dumps out of overdrive capability. The unit has a hill holder feature and cannot be operated in OD mode in reverse. These units have nothing to do with Borg-Warner units of the same vintage and no parts will interchange. They are also much more rugged than the BW units.
Should the Tiptoematic feature not operate, don't despair, the overdrive can still be used. But if you can get the TTT to work, it will truly be a joy to own and operate.