I know the definition of space-like and time-like coordinates in simple geometric, basically, we got: $$ds^2=dt^2-dx^2-dy^2-dz^2$$ so the coordinate with a positive contribution to the $ds^2$ is the timelike one, so far so good. but is it always the case that the metric has a $(+,-,-,-)$ form, so that the sign for one of them is different from the other one? what if I have a metric like $(+,+,-,-)$, then what would be the timelike one?
PS - I don't have a formal education in theoretical physics and I am self educating myself through various text books, any source or guidance is greatly appreciated.