Sony's lineup actually has support for precisely that in the pinout of the MI Shoe which all their cameras since over a decade use [1].
Unfortunately, the <insert swear word of choice> at Sony never released a GPS dongle, and while there has been root available for all Sony Alpha models up until the A7S2 via the integrated (fossil and cut-down...) Android subsystem and they all run Linux, to my knowledge no one has reverse engineered the MI shoe comms interface, how to get that ruddy thing into being a wifi client instead of that temporary hotspot crap, or how to make it behave like a goddamn normal UVC webcam over USB instead of needing their brutally unstable client app.
Sony makes truly best-in-class hardware (no one else has a competitor for the S series in a low-light scenario) at the best possible price point... but damn no matter what hardware they're dealing with, they're the typical Japanese company that cannot get software right.
Rant over.