Wouldn't be too hard to muck up the code so that both LEDs can be on at the same time.Well here's the alternative micro version (picaxe, arduino). Assuming said micro inputs have pull up resistors. Overkill? Maybe when you compare it to the Apollo computers.
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A J/K master-slave flip flop might do it, but you have to scrutinise the truth tables on the data sheet to see how it responds to "illegal" input combinations.