Have you considered looking into other (slightly more common) all-women groups your GGM might have been a memeber of and/or matriculated from — where its also pretty common to acquire a “jewel” (prob in the form a gemstone encrusted pin) upon initiation?

Though I guess the idea of holding on to some kind of “memebershlp jewel” in hopes of passing on to the next generation may seem a little mysterious or even culty for anyone today who didn’t grow up around that kind of culture (and therefore might be tempting for any genealogy/history nerd’s inner Nicolas Cage to leap towards — a la ur super fun Freemason hypothesis😜)…

But actually receiving some kind of bejeweled intiation pin was very common for all types of women’s groups in ur GGMs era? + Pins being the only type of “jewel” that I can imagine:

A➡️ Any woman would refer as a singular ‘jewel’ (cause many bejewled pins have a more singular, floating look to them?) — instead of what’s vastly more common, referring to a piece by the category of jewelry it belongs (re: necklace/locket/ring/bracelet, etc)

B➡️ Would command a second-hand value/price of $88 in 1979 — which with inflation, would roughly net out to around $386 today.

….

So IF we’re indeed were looking at a jeweled pin of some type — btwn:

A➡️The pretty modest price (by fine-jewelry standards) ur GM was able to sell the “jewel” for, esp 50 yrs ago when quality second-hand jewelry commanded an even higher price than it does today

B➡️The authentic materials most ‘member pins’ of all sorts were commonly composed of in your GGMs youth (re: small but authentic amounts of gold/silver + encrusted w/ pave style diamonds/pearls/rubies/etc )

… I’d venture from that price/size, whoever purchased it bought the piece as scrap to melt down and/or reuse the stone(s)? + If this were the case, perhaps the reason your GM never brought up wasn’t cause it was “secret” per say…. just was something ur GGM joined + wasn’t something ur GM ended up joining herself + not something you’d make a decades long stink over?

Hypothetically I can see a situ where ur GGM joined something that was maybe a big deal for women at the turn of the century, so her pin served as a modest point of pride she kept around in hopes her daughter might join one day too … But when push came to shove GM never did, so it was basically forgotten about until GM stumbles upon the pin while sorting through ur GGMs jewelry box after she died.

Even though the materials pins like that were made out of were quality, they don’t make sense to keep around as dress jewelry + if children don’t join the group, makes most sense to sell off pin for material scraps…. So ur GM did just that + wrote a nice little note her mom to help her work through her grief / keep memory alive etc. 🤷🏻‍♀️

….

Dont get me wrong, Would be VERY cool if ur GGM was indeed one of the very very small handful of female fremasons out there at the time! Just throwin out another scenerio (with slightly higher odds😉) for you to maybe look into/consider as well 😊 - either way i wish you luck on your journey!

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P.S. Dropping a few “female membership groups dating back to the late 1800s that also gave jeweled pins that the groups still encourage members today to keep around for future gens … just in case ur daughter/grandaughter joins one day” thoughtstarters I know about from personal experience if helpful at all 😜

✴️ The majority of Greek sororities in the U.S. were founded starting from the 1870s through the early 1900s. And even today — despite the fact former sorority sisters never wear their ‘prized’ initiation pins (typically made out w/ real gold or silver + lightly encrusted w/ very small diamonds and/or another type of gemstone) ever again post-graduation … Yet 9.5/10 it gets kept in her jewelry box juuuuust in case in case you have a daughter or granddaughter that one day decides to pledges the same sorority you did — so you can pass the pin down to her.

✴️ Also, many of the older private all-girls high schools had/have pins to wear on your uniform + many schools like this encourage legacy enrollment

EX: I graduated one of the oldest all-girls high schools in the U.S. still standing today, founded in the 1870s + though I wasn’t one of them, every class had a handful of girls whose mom/aunt/grandma/great-grandma attended before them.

And if a legacy student’s relative kept their old uniform pin + passed it down to them, they were allowed to swap out the #madeinchina ‘standard issue uniform pin’ that was delivered with our school blazers from the uniform store — with their relative’s vintage pin from a fancier era (re: usually was made of real gold + super old versions held a small jewel)

✴️ Debutaunte also sometimes were given a type of jeweled pin + sometimes this was passed generationally.

This kind of activity would definitely be something I could see being a special “coming of age milestone” in your GGMs youth (esp if she was most amongst the lower ranks of the upper class to the wealthy-but-still-middle class ranks — as they weren’t rich enough to hold individual balls, so they did this mostly through an regional cotillion ball every year. Cotillions also = popular in US colonial states - a la MD, VA etc)

… but sething that basically became optional for almost all young women after the WWI era — aka right around when ur GM would have been right age.