If you are calling to find your replacement, your are not doing this of your own free will for your own enjoyment, you are doing it to benefit the company. You are literally doing work for the company on your own time. Doing work on your own time is wage theft.
Call in sick when you need to, but finding coverage for your absence is not your issue. That's management's job. They need to do it or they need to pay you for the time it takes you to find someone. They even need to pay you for your time if you try to find someone and can't. If they are not willing to pay you, then don't do it.