OK, well, we can just skip over the historical recounting; what your photo shows looks to me like an original finish that's flaked/been scraped off, exposing bare brass that's turned brown, as bare brass does.
Gold plating is almost always going to have a coat of silver plating under it. Your photo shows no evidence of this, so it's almost certainly not factory-applied gold plate.
It is possible that it's been gold plated aftermarket and not done very well, i.e., without the standard silver (or other) flash undercoat. But I don't think this is the case.
I think that what you've got there is original (or refinished) lacquer that's flaking off. Under the lacquer it's keeping the brass shiny, and where the lacquer's come off, the brass is turning brown. Usually, old lacquer turns brownish too, which makes me suspect that this horn's been refinished, using a more durable lacquer that is less prone to turning brown; but maybe the surface prep wasn't very good, so the new lacquer is coming off.
Full-body views of the instrument would go VERY much further in assessing the probable nature of the finish.
So-called "red rot" is a normal version of oxidation of brass with an unnecessarily inflammatory name. When brass tarnishes it can form one of three different oxides: green (verdigris), brown, and red. It's extremely common for a single brass article to show all three of these. In the case of a saxophone the red form is what some have recently taken to calling "red rot".
The REAL "red rot" phenomenon is something that occurs in the lead pipes of trumpets and trombones where you have a long small diameter tube that's constantly wet on the inside, and corrosion can lead to pinholes in the tube, which will then have to be replaced. This doesn't happen in saxophones because the tube is so large, and pierced with large holes down its length, that it dries out and doesn't stay constantly wet on the ID. The reddish corrosion you'll see on a saxophone may look unsightly to you; and if you rub it on your white shirt it will make an orangish stain that's difficult to get out; but it does not presage some kind of imminent destruction of the horn. At least, not for the next few hundred or thousand years.