I have found the following after observing several births from my fish.
The dark gravid spot will become even darker and move closer to the cloaca. This is not always a sure sign though because some fish do not have light enough scales to view this. Also if the fry are white for example, then there won't be much of a gravid spot. If there is, when it is close to the cloaca, the birth will be soon.
The female may chase the male around aggressively.
The female may hide in a secluded area from the rest of the fish in the days leading up to the birth.
The female'a vent will transform from circular and rounded to square. This is because the fry are moving closer to the cloaca for the birth. The back fin will also become level with the front of the fish, dropping down.
The cloaca will become dialated or pea shaped in preparation for the birth. This means it is very close. Do not confuse this with constipation.
As for when to pinpoint the birth, I have found using a combination of watching for hiding behaviour, looking for the squared vent, and finally confirming with a dialated cloaca, all lead me to believe that the fish will definitely give birth. I usually only use the gravid spot to determine pregnancy.
If you are going to put the fish in the breeder box, which I do not recommend unless you are absolutely sure it is time for the fish to give birth as it may cause stress and cause a premature birth, I would wait even a day after you think she will give birth. If you are truly afraid of the other fry being eaten, then it is better to put her in the same day.
Birth will usually occur overnight, in the dark.