Say I wanted to file an amicus curiae for an upcoming SCOTUS case; where would I go to find the deadline to file? I've looked on places like SCOTUS blog, Ballotpedia, Oyez, Wikipedia, and found nothing. Am I searching wrong?
Supreme Court Rule 37 places the deadline to file an amicus brief in support of certiorari at "30 days after the case is placed on the docket or a response is called for by the Court, whichever is later." The Court doesn't generate briefing schedules for each case, so you have to calculate those dates yourself.
A case is "placed on the docket" upon filing of the petition for certiorari. Respondents are not required to file any response to the petition, but in some cases, the Court will ask them to do so. Both events will appear on the Court's online docket, so you can find those dates and add 30 days.
For instance, in Kowall v. Benson, the Petitioner filed for certiorari on April 15, 2022, so the deadline for an amicus brief would have been May 15. But on May 31, the Court asked the Respondent to file a response brief, so that kicked the deadline out another 30 days, to June 30.