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An offer to join the GA Club was included on all GA packaging. Other than the offered pin badge and membership card there appear to have been no other member benefits, but I'd love to hear from a former member if there were!
As a note, the GA Club will have inspired the idea for a similar scheme in Britain. Suggestions for such a Spacex club were requested in British advertising during the summer of 1970, but there's no evidence to suggest this idea was ever developed.