If I'm understanding correctly that it's the father and the aunt whose common parent you're trying to figure out, and both the father and the aunt are in GEDmatch, compare their X-DNA. The father only got X-DNA from his mother and the aunt from both her parents, so their X-DNA should match if they share a mother and shouldn't significantly match if they only share a father. (ETA: Unless their mothers are closely related, but that's a whole other issue.)