To chase your tail means to take action that is ineffectual and does not lead to progress, and in this sentence Briggs is mocking the person for taking such action.
Consider the statement ""But it's been so much fun watching you try fruitlessly and making no progress," Briggs mocked, still keeping himself hidden behind his black magic.". Based on this ""But it's been so much fun watching you chase your tail," Briggs mocked, still keeping himself hidden behind his black magic." a true statement? Yes, no, or I don't know?