Yes. As you did under-dash, that switch simply shorts the black horn wire to gnd. But, since the steering wheel turns, it routes thru a copper roller on the turn-signal switch, which can break off. To test that path, try shorting the black wire in the photo to the steering shaft. Also, in some cars like my C-body and I think E-bodies, the steering shaft is rubber-isolated so needs a jumper around the RAG steering coupler in the engine bay, but not true in A's since it gets thru the all-metal coupler fine.