It’s the opposite of “couldn't make heads or/nor tails of”, and the logical opposite of NOR is is OR.
“But then, all at once, for some apparent reason…” might be the opposite of “little by little, for no apparent reason…”
“But then, all at once, for some apparent reason…” might be the opposite of “little by little, for no apparent reason…”
this that | this or that | neither this nor that
----------+--------------+----------------------
T T | T | F
F T | T | F
T F | T | F
F F | F | T