A lot of "old skool" guys always told me a rule of thumb was L/D > 2.5 or > 3. This would give sufficient sufficient support for side loads and bearing stresses. At the same time the >3 engagement would provide stability along the axis of the dowel.
Where they got those values I have no idea. Maybe a deep dive into Machinery's Handbook would turn up a clue or two. Most search engines like Google are utterly useless for this kind of stuff.
TygerDawg
Blue Technik LLC
Virtuoso Robotics Engineering