Here’s some tips, later in this linked post, written within the month.
The function specification is an automatic part of the system message and is in a special format the AI has been trained on.
With the lack of attention that latest gpt-4o pay to context, especially with growing conversation, techniques like injecting post-prompt reminders after user input about the utility of functions, or even reproducing again the output schema for a structured response, start to become workarounds to poor quality.