I have this object:

I want to select all the faces on the edge of the squarish cut-outs of sphere, so I this desired result:

That was done manually, but there must be an easier way.

Essentially, I want to select the faces that have normals that point tangential to the curve of the sphere. Phrased another way, I want to deselect the faces that are facing inwards/outwards, leaving only the desired faces.

I know if I hit SHIFT-G, I can select by similar normal, but that gets me the global normal of the face points, not the local normal.