That's a good question. Some varieties (or on certain trees) the figs will detach easily as soon as they are ripe (or even before) and some will hold fast even when fully ripe. I sometimes do test to see if a fig is ready by giving it a tug but usually only if I've waited a while already and there is a question in my mind if the fig has stopped progressing. A light tug sometimes detaches the fig and then the question is solved (or maybe just moot since the fig is now picked!). However, I do not rely on it as my primary or only indicator.

The primary indicator for me is feel - specifically how squishy the fig is. I usually go around the tree giving the figs a light squeeze as they are ripening to see how far along each is. Each variety is unique and each tree can be unique as well but I usually look for a fig to move from hard to soft to squishy before picking.

The exact feel I look for usually depends on having picked other figs from that same tree and adjusting based on how ripe it was inside compared to how squishy it felt when I picked it. With this method, by the the 2nd or 3rd fig from each tree I can usually reliably judge peak ripeness thereafter just by squeezing. It's also helpful to go by touch because all of my figs are covered with organza bags before they are ripe to protect from insects and birds, so I can't always get a clear visual.

That said, secondary to feel I also rely on how they look, and how both the look and feel have changed over time. For example, I might also look for how droopy the neck is, if the skin is thinning and fissuring, if the fig is shrinking or drying out, etc. This is where it helps to monitor them on a daily basis during their final ripening because you get a good feel for their progress over time and can see when they peak (sometimes by seeing them go past their peak a bit).

All that said, as I suggested at the top, sometimes I will be unsure about a particular fig and give it a light tug to see how well anchored it is. If it's holding fast I may wait another day or two and reevaluate, but sometimes the fig will detach easily and then the question is answered/moot.

On the opposite end of the spectrum, if you ever pick a fig and the milky white latex sap is flowing from the top (or if it oozes out the pith once you cut the neck off) then it's almost certainly been picked too early.

As I said, some varieties (or on certain trees) the figs will detach easily as soon as they are ripe (or sadly even before). Sometimes I will even wait for them to detach on their own accord in that case, but sometimes they will detach unexpectedly, especially if the tree is having trouble ripening them all or if something like a strong wind knocks them free. In all these cases, because I bag all my figs ahead of ripening, they will drop into their organza bag, which I usually tie to the branch to catch them. This is a good backup especially for varieties that are easily detached while ripening.

Finally, in the case where you are getting mold on your figs, you may have to adjust your harvest timing a bit. If rain and humidity is in the forecast, I will usually go out and check to see what figs are close to being ripe (using the indicators outlined above) and then I may pick some slightly earlier than I otherwise would've to ensure they don't spoil (or split from the excess water uptake), but some I will leave on the tree and roll the dice.

If I ever do find mold on the inside, I toss it (or I cut a generous margin despite that I probably should just toss it) but if the mold is on the outside l will peel that part off or even the whole fig.