Is a pitcher the only player allowed to wear a jacket while running the basepaths?

I have never seen a position player wear a jacket while running the bases, but could they if they wanted to?
Is there a rule that says a pitcher can and a position player cannot?
Interesting how the question is answered both ways.

Yes the pitcher is the only one who can wear a jacket on the basepath, and there is a rule governing this.

Edit: It depends on the rule set how the rule is stated. It is stated explicitly in NFHS rules that ONLY the pitcher may wear a jacket while running the bases. All other players must be in regular uniform. I will try to find a link for you.

Edit: It’s not in OBR but NFHS does express it. There is no link, you just have to have the book because they don’t publish their rule books online.

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