We were always taught that it was spelled “gauge”.
It looks like “gage” has been added on as a variant of “gauge”, the original spelling, for instances in which “gauge” would be used… except for the knightly challenge thing, some sort of plum (greengage), pledge, etc. Those are only “gage”.
With few exceptions, I’d also say that ‘gauge’ is the more standard spelling – at least in AmE. To me, ‘Gage’ is more likely to be someone’s last name.