I have last year's version of the NFHS rule book. The non-contact unsportsmanlike conduct by nonplayers rule (rule 9, section 8, article 1) does not specifically mention bands or when they may or may not play during the course of the game. Examples are listed within the rules (for example, profanity, disrespecting a game official, unauthorized conferences, use of tobacco, etc) however the rule specifically states that penalties are not limited to the examples listed, so it's up to the discretion of the game officials.
There's nothing I can find at the TSSAA website that specifically addresses this either, so again, it appears that everything points back to the discretion of the game officials as to whether or not the band playing on would bring out the yellow hankies.
Hope this helps.