I'd like to draw a distinction between a toll "tag" and a transponder.
Here in Louisville, three bridges are currently tolled after the Bridges Project, which entailed two all-new bridges over the Ohio River, and a tolled, rebuilt third bridge.
The tolling authority offers two automatic payment options;
A conventional active transponder and,
A passive "tag".
The transponder is, indeed active, responding to a query by the tolling transmitter mounted on the bridge superstructure with an answer identifying itself as being associated with a particular account. This transponder can be moved among up to four vehicles that have been pre-registered as belonging to that transponder.
The passive tag is simply that; a paper-thin plastic tag with a bar code printed on it that is to be mounted on the windshield, and read by the (supposedly) high-res cameras mounted on the same superstructure as the transmitters. The tag is good for only one vehicle, and so cannot be moved between vehicles. I've been unable to ascertain if there is a RFID component to this tag.
I do believe OP is using a transponder instead of a tag, as a tag would not work if it's strictly an optical device.
This (and the CLICKY) does answer a question for me though. It seems that a transponder will most likely work if it's contained in a jacket pocket or other thin-walled enclosure, as long as orientation is optimal.
Good Ridin'
slmjim