No pano roof here so, can't answer that. Still having to stick the transponder out the window through the ~50 mph carpool lane of the Dumbarton Bridge. By the way, had to go through the 25 mph regular FasTrak lane (with a narrower canopy than the carpool one) of the same toll plaza the other day (with no passenger) and tried the transponder on the spotted area to the right of the mirror stem and it beeped just fine! So, the speed and/or proximity of the sensors in the canopy may have something to do with it too.
Regarding requirements, an EV is equivalent to a carpool even when driving solo and both have to use the transponder or (occasionally) rely on the plates being recognized through bridge toll plazas. The same carpool hours apply. You do have to "hide" the transponder in the HOT lanes (such as 237) and you can ride in them solo with the HOV decals; an external transponder would put you at a disadvantage here.
The Fastrack instructions say to save the mylar film bag it comes in and put the transponder in the bag when you go in HOT lanes. The sensors won't see the transponder and won't charge you.
To make it clear, you have to have a Fastrack to use the bridge toll carpool lanes and you do pay a discounted toll. It used to be free and no transponder was required. But that changed a couple of years ago. If the sensor doesn't see your transponder, they will take a picture of your license plate which has been registered with your transponder and just deduct the toll from your balance. This is true for anyone with a transponder that doesn't get read. A few years ago I had a transponder whose battery went bad and it would never beep when I went through the toll plaza. However, I still got billed as if it had read the transponder. If you go through without a transponder and don't have one registered to that set of plates, then you get a big ticket.