You asked... "how could some of the jacks remain unconnected? If they remained unconnected, then their output side would go nowhere! It would not be left as its own code, it would produce no code at all!
I believe that "unjumpered" letter jacks, are connected to themselves, mechanically. Plugging in a pair of banana plug, breaks the "self connection" and allows for the input letter, say, A, to become, say, "T". If a letter jack is unjumpered, then pressing "A" results in "A" being fed into the static wheel. Also, if the output is "A", then the plugboard passes "A" to the lightboard. At least this is my thoughts on it...