Perhaps you have to choose the audio track such that you don't fall asleep.

Yes, the track matters. A good track for non-sleep deep rest will have you set an intention not to fall asleep and then keep your mind busy doing a body scan. I was the same way... skeptical I'd stay awake. But it actually works.

Try this track https://open.spotify.com/episode/0LXBzjxhdJDFiW2CWINGb3