I have multiple gauges with varying curvature. I fear that if I use a flat stone, the curvature might get irregular.
ceramic rods
touching up regularly to keep gauges sharp is much easier than dulling the edges and needing to resharpen
veeeeery carefully
jokes aside, an outside radius you can do without a problem on a flat stone, on an inside radius either get yourself a round stone, or wrap sandpaper around a dowel
Find someone with a Tormek sharpening system with the woodturners kit, and beg to use their Swedish shapening marvel.
Mini belt sander/sharpener, belt should contour to the blade shape. I got a cheap one from Amazon works well for most tools.
https://www.amazon.com/gp/aw/d/B07CVN8HV5?psc=1&ref=ppx_pop_mob_b_asin_title
belt sander removes too much material very quickly
Variable speed and fine grit. I have used the one I linked a ton to sharpen all sorts of tools. Also it’s literally listed as a tool sharpener.
Convenient way is sandpaper and a dowel of a similar diameter of the gouge. The best way is to get gouge sharpening stones because I hate sharpening on sandpaper.
