How to give patterns to Simplify's assumptions?

How about this?

Power[sign[x_], n_?EvenQ] ^= 1;
FullSimplify[Sqrt[1 - Cos[θ]^2/sign[r Cos[ϕ] Sin[θ]]^2]]

A combination of TranformationFunctions and UpSetDelayed (for the pattern matching) is useful here.

t[sign[x_]] ^:= 1

FullSimplify[Sqrt[1 - Cos[θ]^2/sign[r Cos[ϕ] Sin[θ]]^2], 
 TransformationFunctions :> {Automatic, t}]   
(* Sqrt[Sin[θ]^2] *)