"Am on tail" is a phrase commonly used to convey the idea of closely following or pursuing someone or something. There are several synonyms that can be used to express a similar meaning, such as "chasing", "hunting down", "tracking", "pursuing", or "trailing". Each of these words brings its own nuance to the idea of following, suggesting different levels of urgency or intensity. For example, "hunting down" implies a more aggressive pursuit than "tracking", which could be construed as a more passive activity. Ultimately, the choice of synonym will depend on the context and desired tone of the communication, but each of these options can convey the idea of closely following something or someone with determination and focus.