Tip from a carpenter…
If you don’t have a stud finder or if you don’t trust it, take the handle of your hammer and use it to tap the wall firmly (not so hard that you mark it). You can feel and hear where the studs are. When you good at it you can find the center of stud or very close. Then, take a finish nail and verify. Find both edges of the stud and mark the middle. The only time this doesn’t work well is if the stud has a deep bow away from you and the drywall is not tight to it. If so, find another stud then measure from that 16” and check.
I would not plunge a drywall saw along both sides of a stud to find center like mentioned earlier. You’re making larger holes than necessary and potentially cutting electrical.