I have been using throgs neck Bridge towing tt (Tv 13 chevy suburban gvwr 8600 and tt 14 outback 250rs gvwr 7600) and there is two different amount being charged each other times. Few times it charged...
Happened to me and they refunded me for the overcharges. Seems that the TT is tall enough where sometimes it trips a height sensor and the toll booth thinks you're a semi truck and charges the commercial toll.
We moved off of LI in 2011 and as far as I know, there is no special transponder....you're either a passenger vehicle or commercial. You should be charged the regular passenger vehicle rate plus 2 extra axles for the trailer.