I'd start at the connector on the back of the effected headlight.
Make sure the spade connectors are locked in the plastic plug and not getting shoved out the back when you attach it to the headlight.
Using a Multi-meter see if you have a good ground on the ground pin spade connector in the plug. (Doubtful this is an issue since the Hi-Low beans usually use the same ground circuit.)
Using the Meter again, check for 12vdc at the High beam spade pin.
The High and Low beam wiring is usually daisy chained so you could have a bad connection at the Functioning headlight plug or where the harness is split to go to the Left-Right headlights.
A simple schematic example:
http://www.vclassics.com/archive/images/lgtrly.gif
The Backdraft wiring diagrams on the early cars are severely lacking. They may have switched from Crayon on the newer cars diagrams, but I have not seen one.