Seriously people, use the fucking fan. It clears away odors and covers up the sounds of your dropping a deuce. If you want to stew in your shit smell and revel in the music of your magical poop plops, do so in the comfort of your own home. If you're a guest and the bathroom has a fan, turn it on. We don't want to share.
I went into a public restroom in a gas station once that was set up with a motion sensor. But I didn't immediately know that. It kinda freaked me out for a bit when after like 3 minutes the entire room went pitch black dark. I thought their breaker kicked off or something, while sitting on the toilet.
If it's gonna be on a timer, it ought to be set for more like 10 minutes or something. I dunno about everyone else, but I don't tend to do much of any significant movement when sitting on the toilet to keep the lights and fan on.
Every sensor I've seen let's you set the timeout, and some of the nice once are actually presence detectors so they won't turn off if you are sitting still.