Amicus Curiae briefs are filed in many Supreme Court matters, both at the Petition for Writ of Certiorari stage, and when the Court is deciding a case on its merits.
Some studies have shown a positive correlation between number of amicus briefs filed in support of granting certiorari, and the Court's decision to grant certiorari. Some friend of the court briefs provide valuable information about legal arguments, or how a case might affect people other than the parties to the case.
Some organizations file friend of the court briefs in an attempt to "lobby" the Supreme Court, obtain media attention, or impress members.
"An amicus curiae brief that brings to the attention of the Court relevant matter not already brought to its attention by the parties may be of considerable help to the Court. An amicus curiae brief that does not serve this purpose burdens the Court, and its filing is not favored." Rule 37(1), Rules of the Supreme Court of the U.S.
Thanks for the information in your post #193.
I will take the granting by the SCOTUS to be a positive sign until further notice. Thanks!