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There will be red paint under the gilding, if it is gild, to make the gold colour stand out.
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Yes, it's a very rare one. I only know of one other. It has the words Manufactured by RCI which is Roberts Cycle Industries where Ernie Clements created the first Falcon in 1956. RCI were bought out by Coventry Eagle in 1959. After that the one you show was adopted and used until about 1978.Is that a rare one? I just had a look online and can only find examples like this:
View attachment 572884
Also, yours has traces of red around the wings which wouldn't go with the ones I have found.
I would agree with @midlife - polish it a bit (then spray with clear lacquer to keep the eagle shining)