Sorry for my late reply. I asked for outside testing via Facebook, and the results are that it always works on Android or Windows devices.
For Apple devices, it seems to work on computers (Mac, MacBook), but not Iphones or Ipads. I've had about twenty iPad/iPhone users report it wouldn't work, with only one exception where it did work. I'm guessing it could be linked to Safari mobile. Most testers report that nothing happens at all when they click on "Use my position" (i.e. no request for position sharing).
I tested this both on Safari and an IPad as well and it works.
The only case I found where it doesn't work is if the user has disabled their location services on their PC or Mobile device. In a case like this they won't get the popup.
So the user must have their location service turned on in order for this button to work.
Thanks a lot, Shane. That seems to be the problem indeed so I guess the only solution is to add a comment telling Mac/Apple users to make sure they go to their settings and allow for geolocation.