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I routinely sanitize the inputs to a function using this sort of technique:

funcI[x_Integer] := Print[x];

But it doesn't work with Booleans.

func[x_Boolean] := Print[x];

func[4] (* doesn't execute, as expected *)

func[True] (* doesn't execute, but it should, right? *)

As a workaround, I can use func2[x_ /; BooleanQ[x]] := Print[x];, but why doesn't the simpler formulation work?

func2[True] (* works just fine *)
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x_Integer is a pattern which catches an x so long as the Head of x is identical to Integer. Booleans have no such head:

{Head[True], Head[False]}

{Symbol, Symbol}

Thus, x_Boolean will not match True or False, since Symbol is not identically equal to Boolean.

You may instead use x_?BooleanQ, which is a pattern which catches an x so long as BooleanQ[x] is identically True.

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BooleanQ[] is new in version 10, so eyorble's approach is what I'll recommend for current code. (A hint that your initial approach would not have worked is that neither Head[True] nor Head[False] return Boolean, which is the pattern you were trying to match in your original definition.) In the old days, this is what I'd do (and using a different example):

func[x : True | False] := Boole[x]

func /@ {True, False, π, xxx}
   {1, 0, func[π], func[xxx]}
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