I can't find anything about 軽松明 anywhere, so I cannot confirm either, but I have never seen or heard of 軽 being read as kara or karakai. Only karu and karui. Looking up it kanji dictionaries seems to confirm this as there is no mention of kara or karakai at all. And since 松明 is read taimatsu, not kaimatsu, I'm going to say that karutaimatsu is mostly likely correct.
If it's a teacher who told you that, maybe you could ask them kindly why it's read that way as I would also like to learn. If it's a friend who told you, maybe you can tell them to stop pulling crap out of their posterior.
Kotobank says: 軽松明(かるたいまつ)
source:
https://kotobank.jp/word/%E5%BF%8D%E8%A1%93-593744
you have to scroll down a bit; it's mentioned under "忍具・忍器" and there it's grouped at (4)
Thanks all for, your time and very detailed answer
kanji reading for 軽
hi guys I am trying to have th ecorrect reading of the kanji 軽 in this sentence 軽松明, I would say KaruTaimatsu, but I am not sure at all. In this case 軽松明, I was told to read it as karakaimatsu but not refference in disctionaries. thanks