WDW CMs have posted that GACs are not used during the character greetings where the character just shows up and a line forms outside (except for children on Wish trips with those types of GACs).
For the character greetings where that is the attraction in the building (like in Toontown), show the GAC to the CM at the entrance. They may have a quieter, more private place you can wait. It may not be a shorter wait, but could be out of the regular line.
For MGM, there is a place where you can meet Mickey for pictures. We did not show DD's GAC or ask for any special treatment, but the the CM pulled us out of line to have DD and one other member of our party wait in a roped off part of the line, away from the other guests. The rest of our party was to wait in the line and have us join them when they got to the front. That did not go over well with DD - she either wanted everyone with her or to wait in the line with everyone. So, we got back into the line.