1966 3 speed manual trans problem. Help!

If you take a look at that picture, you will see that the low-gear slides back and forth on the mainshaft, to engage either reverse or first. Notice that the gear is helically cut. That means it will want to jump out of gear by design. The only thing that keeps that from happening is the detent on the shift-lever. Also notice that it takes a pretty long travel to go from neutral to engaged.
You describe a not-long-enough travel into first, so either there's a linkage problem, or the L/R lever is too long. That's my guess.In any case, I'm pretty sure the problem is external.