How much for an overnight babysitter??

I ask this after my child was awake for 4 hours in the night and I’m going insane. Low cost of living area, average daytime babysitter $12-15/hour. For a 13 month old that wakes up 1-2 times per night am I paying hourly or nightly? Not expecting them to stay awake all night, just get up when he gets up. Like a 10-12 hour shift once a week. I’ve seen a lot of people say they charge just a flat overnight fee but is that just for kids that never wake up?