We do the same thing with the timer on our kitchen stove for sharing! It works like a charm. As the children get older we let them have some say in deciding how long each turn should be, that way it gets them thinking about solutions to problems rather than depend on us to break up fights.
We set the same timer for time out. When the child is angry about being in time out, it helps them to focus on waiting for the beep rather than directing their anger at parent, they learn to see that they caused their consequence rather than “mom and dad are making me sit here!!!” We always say “You decided to break the rules by doing ********, so now you have to wait for the beep.” Then when it’s time to get up we talk to them about what they did wrong and how they can make ammends and what they will do differently next time.