How about this: Lord E questions Baxter's sanity (canon), brings in Sir Roderick Glossop, who Baxter has consulted (canon), G knows B is sane, so he spends time gossiping rather than examining B (I always thought G very indiscreet about his patients, telling Bertie about the man who thought he was a canary), G is also 'treating' Bertie and let's slip something that gets Baxter thinking. Or G could say something more general about people in love often repressing their feelings from themselves, and B goes on the hunt for repressed feelings and finds them in all sorts of places, some of which are way off the mark, so its just by chance he gets it right with Bertie and Jeeves.