Is there actually a 15 min tow time limit in towing power mode?
In short No!
There is a battery test switch primarily aimed at tow crews. Pushing the test s/w gives an indication of battery charge state.
The three lights are: High approx. 60 mins available. Med. approx. 30 mins and Low approx. 15 mins.
As said earlier the operators wanted to be able to tow without the use of the APU or other external power source.