This is from MTH "3-rail locomotives equipped with the all-new Proto-Scale 32 feature can be operated on 3 or 2-rail track under AC or DC power. A small switch will redirect track power from the center rail pickups to the locomotives left side drive wheels. Ground will move from all locomotive wheels on 3-rail operation to the left side locomotive wheels on 2-rail track." (this does not make sense to me - one should be left the other right - i am probably missing something in translation)
I have the new oil version, runs great no issues on 3 rail. Sounds to me you have your outer rails electrically isolated. Presumably the switch in 3 rail position will flow current out through either wheel on any particular axle. From what you describe that is not happening. So when you run 3 rail you would need to provide a connection between the TIU and both outer rails or provide a connection in another place such as a normal 3 rail car as you describe. It may be worth flipping the engine around to confirm you have a ground issue. Should work fine one direction and have issues the other direction if the outer rails are isolated. I suppose it could be a faulty switch or a loose/broken ground wire connection. If there are diodes in the circuit you will not detect continuity between the wheels.
This feature has been around a long time, maybe one of the forum techs will show how these are wired.