The best admissible evidence is for you to prepare that video that accurately records the time of day applicable to your case. Also, the school may know the hours the 20 mph limit applies so you might phone there.
The school zone lights are typically tied to the time just before that school opens and the time when it lets out (but may be longer period if it's a high school since students come and go and various times near the end of the day). Normally, I would advise someone to make an open records request to the City of Austin requesting this information. You're probably entitled to it, but there's no guarantee that you would get it back before your next court date. Your best bet may be to find the school start and end times and, yes, sit there with a video tape.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.