Amber,
Do you mean white latex sap, or amber honey sap? Some figs will drip honey from the eye and some won't. Fig ripeness is kind of trial and error. Every fig is going to be a little different. I would think that softness would be a good indication of ripeness, though. Depends on how soft I guess. If it still feels rubbery at all, it may not be ripe. A lot of figs will feel woody, then rubbery, then very soft, kind of like a banana. If you have some doubt, you could just leave it and watch it for a bit. If it starts to droop a little, most folks would say that it is definitely ripe. Is it a fig that sours easily? You can always post a pic with the fig type and many forum members who have been growing and enjoying figs for years will be more than happy to help you. Whatever you decide, I recommend taking a knife and spitting the fig lengthwise and examining it before you eat it, not for safety, but so you can enjoy the fig more and take in all of the color, scent, and flavor of your fig. It will also help you judge the ripeness of the fig in the future. I know this probably wasn't very helpful.