I like your idea. I use to use my watch and time 1-2 mins between sets depending on the exercise. One day I forgot to switch to my sports watch and I had go by feel. I rested until I got my breath and heart rate was some what back to normal. It depended on if its high volume or going heavy.i would say don't "time" it per se. judge when to do your next set by how your body feels. i go again when my breathing returns to normal, and the time that takes has gotten less and less, since i've started doing it that way.
High volume I would not wait as long. When going heavy I wait as long as I needed to get the next lift up. It's a good indicator.