Pitted Brass
It is probably my imagination, but it seems to me that pitting on instruments is more likely to be more pronounced on instruments that have been lacquered.
Or it could be that the lacquer was covering inferior brass.
Or, that you are just more likely to notice it since you are more likely to be trying to buff it off a brass horn rather than a plated one.
The same happens with some silver-plated instruments.
The pits start from outside, generally they would not be caused by faults in the brass. It is rather faults in the lacquer/plate.
Pits are most common in places with contact to the players hands, it might be sweat that can penetrate microscopic cracks in the lacquer/plating, it gets to the surface of the brass and a corrosion process can take place. Drying off the horn, or even washing with fresh water will not make any difference, neither cloth nor water (because of the surface tension) will get town in the faulty place. Even microscopic amounts of salt/sweat can make a pit.
I also see brass pitted from what appears to be rust. You can usually polish most of this out but it takes some work. It has a black color. Does anyone know if this is a rust like you would get in steel? I am not a chemistry expert.
What you have seen sounds like remainders from water drops. When an instrument without law, or with poor law has been played in rain, or got wet in other ways, and is laid aside for a longer time without having been dried, brown marks will build up on the brass.
They are indeed difficult to polish off, and in some cases, marks can be seen in the metal if they are polished away.
Old wise words say that one drop of rain costs ten drops of sweat if the instrument is not dried after having got wet.