It depends on how the rock is turning brown. If it's turning a "natural" brown (gradually turns brown over a period of time), then that's fine. If there are brown splotches on white rock, that's different. TBH, I'd just leave it and do bigger water changes. If it's the "fuzzy" brown algae, a toothbrush works wonders, just make sure to have something that catches all the brown dusty stuff you brush off. I do it in the tank, and the filter sock/protein skimmer takes care of it. Then I do another water change.
SSB(shallow sand bed) owner here:
I tried doing a sand siphon once. It did suck out a ton of crap. However, you don't need a sand siphon, just a good old fashioned gravel vacuum. You just have to kink the hose and keep it kinked with one hand, controlling how much water is sucked in at one time. HOWEVER, I would not recommend doing a large sand siphon. Maybe just 10% of the substrate at a time (this allows for repopulation of the sandbed by other critters you like such as bristleworms, copepods, amphipods, bristle stars, etc.). You WILL have a nutrient and thus algae spike. I'm going to do one on my tank in a few months (about a year after it got established), so that there's not too much fauna-unusable nutrients in the sandbed. But if your tank is new, I don't think that siphoning the substrate is going to do much good (probably a lot more bad than good actually).