First, don't waste any time looking for OhioGal's "'local rules' for the South Dakota Supreme Court" as there aren't any "local rules" applicable to practicing before the highest court in any state, including OG's home state of Ohio!
Such a reference is as ignorant of the subject as saying that the Rules of the United States Supreme Court vary from state to state and territory to territory.
If you want to read the rules governing all appeals to the South Dakota Supreme Court you will find them beginning at Section 15 26A of the South Dakota Codified Laws entitled: The South Dakota Rules of Appellate Procedure. They apply equally to Aurora and Yankton County, South Dakota and all political subdivisions in between.
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Secondly, although there is no specific language in these appellant rules contemplating the filing of a motion to dismiss an appeal because of the default in a timely filing of the appellant's brief it is permissive to do so.
However, it is to be noted that the timely filing of the appellant's brief is not jurisdictional; that is, it does not per se deprive the court of jurisdiction to rule on the merits of the appeal as would be in the case of a tardy notice of the appeal.
In other words, it is a matter of judicial discretion as was held in the SD Supreme Court decision in Dubray, Appellee, v. South Dakota Department of Social Services, Appellant, No. 23241 (Dec. 2004); to-wit:
"Thus, DuBray timely filed her notice of appeal, but she failed to timely file her brief and that default was excused for good cause shown. This Court has previously stated that under our analogous rules of appellate procedure “only failure to timely serve and file the notice of appeal is jurisdictionally fatal to an appeals validity, while lesser omissions may be subject to sanctions.” Western States Land Cattle Co., Inc., v. Lexington Ins. Co., 459 N.W.2d 429, 432 (S.D.1990). "
It is also worth of noting here that Dubray was 135 days late in the filing of her opening brief!