"The running lights are on and the relays seem ok.

"Seem" is the key word. If the headlight relay clicks when the switch is turned to position II, and the running lights stay on, the coil and one contact are OK. But if it has lived in a damp spot for all these years, I'll bet you can open the case and find that the (harder working) headlight contact is missing.

"Could it be the bulb failure circuit ?"

Not if the High Beams are also out. Only the Low beams go thru the BF sensor. As i said, it's a single "headlight" wire all the way to the fender rail relay. From there the red wires go straight to the High Beams. But the Blue wires get routed back inside, thru the BFS, then back up front to the lamps.
--
Bruce Young
'93 940-NA (current) — 240s (one V8) — 140s — 122s — since '63.