I've been involved with many boards, both as advisor and member and the
phrase I've most often heard is "Friend" raiser; you know like fundraiser, but
different. This terms is used to reference mining new friends as general
members to the museum, not a special category of museum membership unless that's
what you're going for. It reminds me of a song we used to sing in
elementary school that went, "Make new friends but keep the old. One is
silver and the other gold." That's my five cents, hope it helps.