JT telling Brad they were voting for Sierra wasn't a bad move, his tribe just fucked it up. Go back and watch it, JT very clearly tells his tribe "hey, we need to switch the vote to Brad, I just told them we're doing Sierra". He says this multiple times and Sandra is just like "no everyone stay calm and stick with Sierra". JT had every intention of double crossing Nuku and it totally would have worked if his tribe listened to him.
Yea but he could have enforced it. Said "vote sandra and ill vote with you, otherwise one of you goes home" Boom done. No idol needed to be played. Sandra goes 6-5.