I had the same issue with my '94 when I purchased it. Since the high beams are working when you pull the stalk you know the bulbs and the relays are working. As jonheld said the problem is in the stalk. I was able to repair mine in less than 30min by pulling the stalk and cleaning the contacts inside the switch housing. You can find all the info you need on mud to remove the necessary dash pieces and access the switch contacts.
Also, if you do some searching here you will find others that have done this only to have it work for a short while. I think the reason some have not been successful in the long run is they clean the contacts and remove all the grease. The contacts are handling a significant amount of current when they ground the 12v power for the lamps. This causes them to arc during engagement and dis-engagement and thus oxidizes the contacts. The dielectric grease is there to coat the copper contacts and prevent current from flowing until there is solid contact. (dielectric grease is an insulator and is pushed aside by the spring loaded copper contacts) It also protects the contacts from air and moisture preventing oxidation.
Once you get to the contacts (not too difficult

) be careful you don't let the whole switch assembly or contacts spring out, it will be difficult to reassemble. Use a fine metal file or embry board to clean the contacts to bright new copper. Apply some dielectric grease and put it all back together.
Also, Dave 2000, I think the flash mode keeps the low beams on and adds the high beams. Not sure but it's possible that the 4 lamp on mode reduces the current draw at the high beam contacts and prevents the flash mode from failing as often.
Hope this helps. It's really a

job. It was the first priority when I got my LC and surely saved me and some deer on my commute.