well I can't solve the mystery, never seen that stabilizer piece, but according to the shop manual the 'stabilizer' should be glued to the glass, which means it wouldn't be felt - sounds to me like it may have been included to take up slack in the track resulting from the crown of the body side .... which would mean some didn't need it, and being glued to the glass would mean after 50 years it's as likely to have been swept under someones shop bench ... I'd say the piece you have is a piece of cats whisker material [only thing I've ever seen with stapled felt] someone stuck in there to tighten up the glass
Bill