"Burning the candle at both ends" to mean being unfaithful in a relationship

Too long for a comment, but not much of an answer: The origin of the phrase is Edna St. Vincent Millay's "First Fig"

"My candle burns at both ends
It will not last the night;
But ah, my foes, and oh, my friends
- It gives a lovely light."

One analysis of this short poem comments:

...there are various things that the candle can symbolize. It’s very likely though that this poem is concerned, at least in part, with Millay’s own sexuality

So there's some support for the notion mentioned in the Q

I've always taken that alternate meaning of burning the candle at both ends to mean the person doing so is two-timing, which means cheating or usually means cheating, but is nonetheless an important distinction because of its word choice.

With "two-timing" in mind, burning the candle at both ends' second meaning became inevitable. It contains an overt phallic symbol (a penis-shaped object) that is burning (a word also used for sexual desire) with two flames (a word also used for "lover," so "two lovers"), each literally (and figuratively) lighting upon and licking at each end of that rigid, horizontal, burning phallic symbol (or phallus), in an analogy that refers to late nights and lots of work, the two principal requirements and struggles of two-timing since even just one relationship requires lots of work and late nights, so twice that! With all of that going on, it's very easy to see how the second meaning evolved. In fact, with how much we humans have sex on the brain, it would be hard to see how that second meaning wouldn't evolve.