Learn English – If it hadn’t been for

Both present perfect have lived and present perfect continuous have been living are grammatically correct and natural in this context, and there is no significant difference in meaning because for 25 years nails the duration.

If you are indeed thinking of making a change, using present perfect continuous in your sentence would indicate (very gently) this intent.

In other contexts where you are specifying a long time, the meaning may have a slight effect on the choice of tense: the present perfect tends to focus on the time that has gone by, whereas present perfect continuous is more progressive, focussing on the situation at the end of that time, for example:

I have lived in this town for 25 years and I have seen a lot of changes over that time - focus is on the 25 years
I have been living in this town for 25 years and I still don't know where the police station is! - focus is on the situation now.

If the time interval is not specified or different, present perfect would more likely be used for longer, permanent arrangements and present perfect continuous for shorter, temporary arrangements:

I have worked here for 25 years
I have been staying with my brother until I can find a place of my own.

Both are fine. The difference is in how the speaker is choosing to frame the event in time.

The goal that France have been looking for is choosing to treat this as an event extending to the present. The goal that France were looking for is choosing to treat it as an event in the past.

Both are grammatical and idiomatic. In this case there is very little difference in meaning.

The people who tell you that it depends on the objective question of when the event or situation finished, are giving you a simplified explanation to try and make it easier to understand; but their description does not match the way that English is actually used.

Many choices in the compound tenses of English (eg the choice of past vs. present perfect, past vs. past perfect, past vs past continuous, perfect vs. perfect continuous, past vs. perfect continuous, simple present vs. present continuous vs. future) do not correspond to objective differences, but to how the speaker is choosing to construct the temporal relationships between events, and often a different choice would be equally appropriate.