I have been told that there is some controversy on this. The Black Hills Forest Service Publication "Working a Mining Claim" states:
"On the National Forest, any activities, including those related to working a claim, that disturb the surface or that require mechanized/motorized equipment (e.g., suction dredges, highbankers, vehicles), require submission of a Notice of Intent (NOI) to the Forest Service prior to the activity, and may require approval of a Plan of Operations (Plan) as described by Forest Service mining regulations at 36 Code of Federal Regulations 228 Part A (36 CFR 228A). Additional analysis by several specialists may be required before a Plan can be approved. This process may take several months or longer.
Permits from state agencies may be needed, especially if water resources are to be used in the mining operation." https://www.fs.usda.gov/activity/blackhills/recreation/rocks-minerals
The controversy lies in what constitutes "motorized equipment". Some will tell you it does not mean a battery operated pump, but does apply to gasoline-type engines. Others will tell you that a motor is a motor. I have also been told that the USFS is relaxing a bit when it comes to battery-operated pumps, as long as the tailings are not being dropped into the creek.
I would suggest you contact the Mystic Ranger Station and see what they tell you.
Mystic Ranger District
8221 South Hwy 16
Rapid City, SD 57702
Phone: (605) 343-1567
Fax: (605) 343-7134
Hours: 8:00 a.m. to 4:30 p.m., Monday - Friday