Unfortunately, they'll need a suspect first - and their phone - to verify they turned it off. The tower doesn't track when phones are turned off. Phones themselves don't store that info forever, either, so there's that...
The
article did mention possibly tracking phones that were active in the relative vicinity, then went dormant, followed by new activity shortly after the abduction. I'm sure they're trying it - and if anyone can pull it off, it's the FBI - but it must be a challenge to do.
This also assumes the suspect, who by all accounts has flummoxed LE so far, was sloppy with his phone usage and brought it with him. It's possible, and I hope that's what happened, but I'm not so sure at this point. Even a simple Faraday bag (or aluminum foil!) can, uh, foil other ways of tracing and tracking, like
Bluetooth Low Energy.
I've explored this phone on/off issue once before with the Kelley Brannon case. We were able to fairly confidently determine that a "target" phone was off because we knew another phone called this target phone at a certain time, but the call did not register on the target phone's call log and went directly to carrier voicemail. (This may not be true for all carriers.) But again, to use this kind of deduction, you'd still need to know who you're looking for.
I hope I'm wrong!