Good find, I've had 2 66 4x's and the one I have now I've had 22 years. Your transfer case can be shifted into and out of 4x up to 50mph from my experience. Remember that 66 thru 70 something F-100 had only in/out type transfer cases with no low range. Get your truck onto an alignment rack so that the front end is 'loaded' but all the front end parts can be checked. I'm thinking your radius arm and track bar bushings are shot and once they start moving around the death wobble starts. I have used urethane bushings with great results as replacements. Other parts like tie rod ends amd ball joints could be a big part of the problem as well.