From How Intersect works—ArcGIS Pro | Documentation
with the intersection set to Polygon and line input for line output
You will get a line as the output. It is just a matter then of querying the line's start and endpoint as to whether it is furthest from the edge. One will be on the edge (Near distance of 0) and the other will be inside (Near distance > 0). Odd cases you probably won't encounter is when the line is exactly on a polygon edge (Near distance == 0 for both)
... sort of retired...