So I used a suction gun and got new brake fluid installed.
The real problem is that the sides are dirty/ caked on, inside the plastic master cylinder reservoir.
I'm thinking of finding a small sponge brush & trying to clean the side walls.
If anyone has an idea how to better clean the dirt away, let me know.

Either leave it or replace it. You will contaminate the system if you try cleaning it.

Yes probably best to leave it as it is.
I may drive it and get brake fluid warmed up, and then just suction it out again.

I'd leave it too. You could try occasionally swapping out the reservoir fluid but it would probably take years of that to have an effect.