The wooden gutter, of typical section, is butt-jointed into the inside angle of a shingled wall with the drain at the other end of the gutter run.  The gutter has an adequate, but hardly vertiginous slope.

But, because of natural movement between the shingle and the open end of the gutter, some water runs out along the shingled wall.  Indeed, although the paint looks fine, I noticed today (at the top of a 14' ladder) that the gutter was nearly all rotted through.  Are you saying the rot is distributed throughout the entire length of the interior of the gutter, or that it's concentrated near the open "high" end?  My guess is that the rot is everywhere, and that the problem is that the paint on the outside of the gutter keeps the water in it from passing through the wood, trapping it behind the paint film to rot the wood.

What was the proper way to finish the gutter end, and block water from exiting the face where the butt-joint meets the shingle?  Seems to me that you either gotta line the gutter (I suppose preferably with lead or copper), or paint it religiously (maybe even evangelically) inside and out, from Day 1.  Alternatively, don't paint it with the understanding that it'll have to be replaced that much more often. Just a lead "skirt" on the inside?  Lining the gutter should be done with plenty of lip (but no smartmouthing!)  to minimize the amount of water that gets back underneath the metal lining, and causing even more rot. Or something else?  I would seriously consider getting rid of the damn gutters altogether, or at least to the greatest extent possible, unless there's a hell of a good reason to spend the rest of your (vacation) life maintaining them. What are the gutters protecting (i.e., deflecting water from), and is there a less labor- and capital-intensive way to do it?