Roos

A very hot goose panting with an open bill can look like drooling too. Not the case in October.

Ordinary mess is water and a bit of muddy liquid dripping after she has been eating or drinking, and the bird is otherwise grazing, walking and honking normally. They drink by scooping and tilting back, they dunk their heads to clean the bill and nostrils, and they mix food with water as they eat. All of that drips.

Stringy and constant rather than after a drink is the version that is worth catching her for. You have described something in between, which is why looking is the right next step.