The phrase "make top of head" is not a common term, but it may refer to guessing or estimating without proper knowledge or information. Antonyms for this phrase could include being precise, accurate, thorough, informed, and knowledgeable. When tasked with a task, taking the time to gather information, research, and understand the topic can help avoid making uninformed guesses. It is essential to have a clear understanding of the subject matter to provide well-thought-out responses, ideas, or solutions. In summary, antonyms for "make top of head" include being knowledgeable, informed, precise, and well-researched.