Ok - still hard to define though. But I'll try.
It's not so much a sign as a feeling. You don't suddenly think 'RIGHT! D.I.V.O.R.C.E'. It kinda creeps up and, if the measures needed to put things right aren't taken, are ignored, then you're beginning to swim without a paddle.
When that happens, the only thing I can say is a kind of whirlpool effect kicks in. Somehow - despite swimming against the current - you're sucked into a horrible, dark and miserable hole.
Now, I'm speaking from MY experience, but I think others' will say its a similar process.
The actual 'day of reckoning', the day one of you ups and leaves, will either be long in coming and kinda expected, or done in haste, panic, when you, your partner or both are at your most emotive. I took the emotive/panicky route. Though it genuinely wasn't intended. I didn't get up one day and drop the bomb. The day started like any other. By the end of it I was out and gone.
I remember going back, a month or so later, to an empty house, to collect my belongs. I was there by 10:30am, out by 16:00pm. I sobbed, every single minute of it. And no, it wasn't cathartic. It was bloody horrible.
Anyway, I hope I've gone somewhere towards answering your question