I actually did some research on this for a book I wrote a few years ago.

A fully powered off phone (not locked, not asleep, not in airplane mode) is generally not trackable in real time. When it's shut down, the cellular, Wi-Fi, Bluetooth, and GPS radios are off, apps aren’t running, and the phone isn't pinging towers.

What causes confusion is that most people never actually power their phones down. A locked phone or one in airplane mode can still transmit if Wi-Fi or Bluetooth is enabled. That’s not the same thing as being off.

Turning a phone off also does nothing to erase history data. Carriers, apps, and platforms may still have past location records.

For normal civilian use, power off means no live phone-based tracking. There are some very special nation-state tracking scenarios where some phones can still be traced even when they're fully powered off, but I don't know how, exactly. The stuff I found in my research was very vague on that (for obvious reasons) and I didn't need that type of info for my story and I didn't want to send out any more red flags than I already had with my searches, so I didn't go down that rabbit hole.

So you were right that powering off was important. I think for 96.93%* of the population that still applies today.

*All numbers are completely fabricated. 😁