According to my math models, It should be about a plus 33% error, so yes, 16/12th error when varying the supply voltage from 12V to 16V
This is of course assuming the gauge itself has no internal regulation and/or compensation circuity for varying supply voltages and is strictly a dumb linear device........I'd hazard a guess that some off the shelf $21.99-$59.99 auto-zone auto meter lesser expensive types could be.
But, thinking a zener diode is a pretty cheap clamping device to slap in to form a sorta decent fixed reference/regulator internal to the gauge, so it could be a crap shoot depending on the manu, so as a test...........
and In theory then to find out you should be able to note a particular level w the engine off and just sitting still, then start the engine and still sitting still, rev the motor up to around the 16V'ish from 12V'ish and see the needle move up and down quite clearly w a possible 33% error as you start up and rev it up and down eh?
I do recall back in the day seeing the occasional needle (not voltage :facepalm

moving around a bit as the engine rev'd, not sure where and who's thou, just think I saw it happen here and there. Maybe it was my parent's 1962 VW Bug
Lower traces show calculated unregulated voltage extents at sender signal out as seen by/at the gauge's input from empty tank(highest levels) to full tank(lowest levels)
Top traces show percent error. given by.......
Percent Error = [experimental value - theoretical value] / theoretical value x 100%