But can "dusk" also mean "the dark part of twilight", where "twilight" refers to the early morning? I'm asking because in my novel, shortly after saying "halfway between dusk and dawn", the author says that one character was trying to shelter himself from the light.
"Twilight" is almost exclusively used for the sunset hours. I agree with GreenWhiteBlue; halfway between dusk and dawn would be the middle of the night. Halfway between dawn and dusk would be midday, roughly around noon.
You can quote up to four sentences of context, including the sentence in question. Can you give us a little context, please?
"Halfway between dusk and dawn, sheltered from the light by the leaning, decrepit ruins, a figure dressed in black came upon the broken whiskey bottle that had once been in the hands of Vic Moore".
It doesn't make sense to me that the author is referring to the middle part of the night, because it was absolutely dark there in the night. It was necessary to use flashlights and there was no point in concealing themselves because of the light.