New to towing vehicle with E-Z Pass question

We just crossed a bridge in Oakland, Ca where the fee is $5.00 per car or $5.00 per axle if over two axles. Crossing with the toad attachéd was $25.00. Had we separated the units it would have been $20.00, certainly not worth the hassle. The real issue is that somewhere in the Jeep is a Fastrac and we didn't want to pay the $25.00 then get dinged for another $5.00 for the Jeep when the Fastrac was detected. We mentioned to the tollbooth attendant and she said she would cancel the Fastrac reading if it showed when we passed, we'll see.