> Does the waw-consecutive have any implicit timing in it. It generally
> describes consecutive events, but is there any idea about the time gap
> between the events?
Nope.
> If there two waw-consecutives are mentioned pretty much one after the other,
> does this mean they _immediately_ follow on? Or does this depend on the
> context?
It all depends on the context. That includes whether there is a
time gap or not, and even whether the one follows the other.