Understandable. It's just my parents HATE having the light on, so alot of times I have no option but to keep it off majority of the time.
They have been peeping loudly constantly and are quiet with the lamp on, yet I have to keep it off unless it's morning. The lamp is high enough so it's not too hot as well.
The chicks are chirpping cause they are cold, need the heat lamp on constant at least until they're at least 6wks old. I understand Florida is warm but these are "babies", explain this to your parents. I live in Hawaii and use a heat source ... Read up on the MHP (heating pad) posted by Blooie, maybe your parents would allow that?
Getting the Save A Chick isn't going to solve your problem, the weaker chick doesn't sound like it's in good condition, it needs the warmth most. Good luck

Maybe let your parents read what we've recommended.