How does a Lemon Battery work?

I have been trying to figure out how batteries work ever since Mr. White (on Breaking Bad) started his van by using ground-up bits of zinc and copper to make a primitive battery. Everyone knows you can make a battery by sticking pieces of zinc and copper in a lemon. But why does it work?

Your Grade 9 science teacher probably wrote a chemical equation something like this, combining the two half-cell reactions for zinc and copper to get:

This would be fine except there is no copper in solution. This reaction works for the fully-developed zinc-copper cell with the copper strip immersed in copper sulfate solution, and the zinc strip immersed in zinc sulfate solution, and the two solutions linked by the "salt bridge". It really doesn't explain the lemon battery. (And it doesn't explain where Mr. White got ahold of copper sulfate solution for his battery.)

A thorough search of the internet confirms that it is the hydrogen ions from the acid, not copper ions, that participate in the reaction. Hydrogen from the citric acid is reduced at the copper electrode, consuming electons and completing the circuit. The copper has nothing to do with the reaction. (Maybe Mr. White used some no-name acid to complete his battery, but the episode was a little sketchy on that point.)

There's still one thing that bothers me. Why does the hydrogen gas only form at the copper electrode? Shouldn't it form just as readily at the zinc electrode? I can't find any explanation as to why it wouldn't, except for this article by Jerry Goodisman where he refers, near the very end, to the fact that Zinc is supposedly a poor absorber of hydrogen.

But if it was hard getting to the bottom of the lemon battery, it is much harder to figure out how the original Voltaic Pile of 1799 could have worked. The story is that Volta stacked copper and zinc discs and separated them with pieces of cardboard soaked in salt water. No copper sulfate, no hydrogen ions...just salt water. I've scoured the internet looking for anyone who has ventured to write a chemical equation to show what is going on, with no success. The closest I found was this article by Franco Decker, who alludes to the difficulties people had back in the 19th century trying to explain it, and concluding that no one was successful until Nernst published his analysis of the reaction in 1890...almost a hundred years after the fact! But then, Decker goes on to analyze the pile assuming an acidic electrolyte. Well, it's easy to see what happens if you use an acid...it's the same as the lemon battery. What I still can't figure out is how it worked originally with salt water.

Any ideas?