I read somewhere that you needed to have the Summerset chapter to research jewelcrafting trraits and that ESO+ membership wouldn't qualify. So I, probably stupidly, spent crowns on Summerset and I still can't research anything but the first 3 traits. I've picked up a lot of jewellery and still not had the option to research any of the other traits.
I have done the quest that opens up the jewelcrafting daily writ but haven't completed the Summerset storyline. Not sure if that's required.