Hey there,
just wanted to share a quick tool i'm using to dye edges with almost perfect accuracy. It might seems a little over engineered but as it is reusable and of great durability I think it worth it.
I tested for a few week the empty markers made from molotow, a german company specialized in graffiti tools.
Here is a link to there pages : https://www.molotow.com/en/applications/marker-applications/empty-marker-system/
Obviously other brands might be available but I tested this particular one. The pens are very well made, the tip is very strong and durable, replaceable. You can load them with spirit based dye and go other you edges with crazy accuracy (both in term of where you dye but also how much you dye as you can control the flow thanks to a kind of built in pump).
The 4-8mm tips seems to be the best compromise (at least for my use).
You mean for veg tan leather not chrome tan, right? Any images of your work with molotow empty markers?