You are correct. Also, if you are in tow/haul and you drop the gear shift from drive to 2, it transmission will lock the TC in 2nd gear. Found this out pulling my 5er up a big hill while watching the transmission temps climb.
Finally, if you have a jake brake and turn it on, it automatically turns on tow/haul mode without having to hit the button. After the engine warms up, the jake brake will not stay on at a stop light.
I leave my Jake on all the time so I don't have to hit tow/haul or look at the dash light, unless my wife is riding with me. Then I turn it off because she doesn't like the firm shifts I get with my Goerends VB and TC.