  In $\tau$-tilting theory, it is often difficult to determine when a set of
bricks forms a 2-simple minded collection. The aim of this paper is to
determine when a set of bricks is contained in a 2-simple minded collection for
a $\tau$-tilting finite algebra. We begin by extending the definition of
mutation from 2-simple minded collections to more general sets of bricks (which
we call semibrick pairs). This gives us an algorithm to check if a semibrick
pair is contained in a 2-simple minded collection. We then use this algorithm
to show that the 2-simple minded collections of a $\tau$-tilting finite gentle
algebra (whose quiver contains no loops or 2-cycles) are given by pairwise
compatibility conditions if and only if every vertex in the corresponding
quiver has degree at most 2. As an application, we show that the classifying
space of the $\tau$-cluster morphism category of a $\tau$-tilting finite gentle
algebra (whose quiver contains no loops or 2-cycles) is an Eilenberg- MacLane
space if every vertex in the corresponding quiver has degree at most 2.
