I know this thread is almost two and a half years old, but when I came across it it reminded me of an
article I recently seen in the Rapid City Journal. The Forest Circus seems to have a chip on their shoulder when it comes to anyone dredging for the sake of mining, but yet if they twist it around in their favor which they did here, they don't seem to have any problem with removing 98,000 cubic yards of sediment from lakes in the Black Hills. Getting a permit to run a dredge in South Dakota is a long-drawn-out, political process and there's a good chance of you being told "no". Dredging is very beneficial to the ecosystem of the creek, both for fish habitats (ironically this was mentioned in the article I linked to) and it's also good at removing the garbage and left-over pollutants from the streambed (such as mercury, which is very prevalent in some creeks around the northern Black Hills), but the Forest Circus along with the South Dakota politicians they're sleeping with don't want to admit any of this if the words "gold" or "mining" are in the same paragraph.
Anyway, to answer your question, 1942 merc, yes you can dredge in South Dakota, but you have to jump through so many damn hoops that you're likely to quit before you ever get there, and if you make it that far you might be declined. I've heard nothing but horror stories on the matter. I've never used the GPAA claims in the Black Hills as I am not a GPAA member, but I have heard positive things about the Husker claim, and I know they've found a little bit on the claims down by Rochford and Mystic (which I believe are named the Mary Ann and the Migg). The Husker typically has running water during the spring melt or after a very heavy rainstorm, otherwise from at least July onward you might find pools of water in the creekbed but that's about it. Their other claims are all on year round creeks if I'm not mistaken. The written word is that you can use anything non-motorized (gas or electric) in the Black Hills for prospecting, so yes, you're pretty much limited to sluicing and panning, and you're also allowed to metal detect in the Black Hills
"as long as you don't dig holes" (gotta laugh at the Fed's technicalities). I don't think you should have any problems with using a carbureted ATV, just use a lower octane fuel while you're up in the hills.