Take a look at the discussion here:
Whirlpool range "cooktop on" light stays on forever
Their diagnosis makes perfect sense, and if you're at all able to get inside the range, it's easy to confirm.
But first, I'd run each of the burner switches on and off a few times to see if the contacts free up or at least maybe the light goes out for an instant when you move one of them, and you'll know which one is bad.
This sounds like a common problem with Whirlpool ranges, as there are any number of Q&A sites that address it, and all give the same answer.