Brackets on pattern test with argument

Question

I am defining a pattern to be used as a test, that itself depends on an argument. For instance, I might want to check that something appears in a given list:

type[x_] := (MemberQ[x, #] &);

I naively used this in the definition of a function and do not get what I expected. Defining

Z2 = {0, 1};
f[x_?type[Z2]] := x

returns f[0] when evaluating f[0]. Putting brackets

g[x_?(type[Z2])] := x

gives the desired 0 when evaluating g[0].

I understand the need for brackets here, as one might want to pattern test an object and then supply it an argument -- (f_?test)[x] -- and I do not mean to get into a discussion about the choice made by Mathematica here.

My question is whether there is a way to define the pattern test "type", so as to avoid the need for subsequent brackets.