Welcome Jeff. Yes, a stock auto trans from that year of Scout would be a 727. For certain identification, it will be a one-piece cast aluminum case. No sense in painting you a false rosy picture here. Normally when an auto trans exhibits this degree of malfunction, the only remedy is a complete overhaul. If it is already out of the vehicle, you're well on your way to that eventuality. If still in the rig and the rig is in running condition, there are a couple things you can check to rule out, but I wouldn't expect a miracle cure. I think your trans is probably in need of tlc.
1. Verify that the shifter cable is properly connected to the linkage on the trans at that the linkage is moving appropriately in relation to input from the selector lever.
2. Verify that all parts of the throttle valve linkage are present and actuating properly. Post an under hood pic showing your throttle linkage and back to the fire wall if you aren't sure what to look for. From that I can determine if something is missing.
3. Check fluid level with the engine at operating temp, rig parked on level surface and idling in neutral. Checking while in park will show a false high level. If the level on the stick is below the safe range, add the appropriate amount of pints to restore a proper level. These units have been known to behave erratically when the fluid level is incorrect.