Personally I would include it just so that the next homeowner doesn't curse you when they go to drill something into an expected stud that isn't there.
this post was submitted on 07 Jun 2024
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For a non load bearing wall, the biggest consideration is going to be hanging drywall which is why you'll see either 16" or 24" OC (to align with a 48" wide sheet). Since the wall isn't meant to hold any weight above it, there's a little more flexibility in where you place your studs, so you're probably fine without that extra stud.
That being said, check your local building code, there might be a regulation for that.
Just to throw a wrench into this post: 19.2" is also valid spacing, as indicated by the mark on your (newer) tape measure.
24" spacing will likely require 5/8" drywall to prevent flex.