I've just purchased a My Laps transponder.  There is a perfect location for it on my car, but it would require the transponder to "see" down through a layer of fibreglass.  (Specifically, the bottom of the nosecone.)  Is that likely to cause a problem?

It uses an inductive process rather than radio waves. Needs clear path to ground with no metal between it and the track.
Fiberglass is ok.  Some liked to put it in the drivers area with a hole in the floorboard. This does not give a strong signal and gives the system problems. The unit is well build as the electronics inside the transponder are completely covered in Silicone. I have seen a few with the case pretty well mangled and still work.