@subnetter @Red-Potato @matty The seminal Gimbutas text is probably The Civilisation of the Goddess, early 90s. I have a copy somehwere, but not in the here in office.
Agricultural societies are without exception patriarchies, and strongly associated with foreplanning, which becomes management and notions of ownership. As livestock becomes part of the process, the idea of owning and managing animals (husbandry) gives rise to the notion of the same sort of management (and ownership) of families.
A matriarchical society almost by definition would have to be free of notions of ownership of this kind, and therefore, have to be pre-agricultural, hunter-gathers, which is how we find the handful that exist.
The presence of female icons/statuary does not imply matriarchy, as the countless tons of statuary of the Virgin Mary or your pagan goddesses of choice from the IE pantheon bear witness to.
As far as fertility cults, this is common to almost all agricultural societies and possibly some advanced hunter-gatherer societies, but again, does not imply matriarchy as much as respect for the uniquely "female magic" of reproduction.