Brifters use relatively long housed cable runs from the brifters themselves to the housing stops on the downtube or headtube and these housings must flex noticably as the bars are turned.

Purpose built shift housing has the reinforcing wires run pretty much parallel along its length and maintains it's overall length as it is flexed. Therefore, it doesn't lengthen or shorten and doesn't pull on the inner wire and change the derailleur position. That stable length under flex is necessary for accurate indexing.

Brake housing has tight spiral wound reinforcing wires which give great burst strength (essential for resisting braking loads on the inner wire) but allows the length to change a bit as it's flexed so it's not as good for indexing. That's also the reason you don't use shift cable housing for brake housing.

The OP was only going to use a very short piece of housing in an area that flexes very little so the fact he got brake housing won't matter.