Neither of your options is correct.
Ideally an acid base indicator would be colorless at one pH and colored after the transition. Such an indicator is phenolphthalein. So when using phenolphthalein it is indeed impossible to detect when all the phenolphthalein is colored. So you titrate to a point where there is the faintest pink color.
So for bromcresol green you should either stop when the solution starts to turn from blue to blue green (ph about 4.6), or as the solution turns from green-yellow to yellow (ph about 5). It would very difficult to judge the deepest green (at about 4.8) accurately.
So which transition you would choose would depend on balancing between which side of pH 4.8 that you wanted to end on, and which transition was easier to detect visually.
You can look at a list of some acid/base indicators at Wikipedia. There are few that go between colorless to colored. Most are color-1 to color-2.
I also point out that you question contains a fallacy.
Should titration stop at the intermediate color or a drop past the intermediate
The burette column is marked "to contain" an amount of fluid along its length. So you can let a partial drop form, then touch the tip of the burette to the flask and get a partial drop of titrant. You don't have to titrate in "quantized" drops.