Sure as heck is unusual - when was the last time you saw a sovreign state submit an amicus brief in a case that did not directly concern it?
This is a case concerning a state law that mandates the verification of immigration status, when warranted. The fact that most of the immigrants [read ILLEGALS] that will be affected are from Mexico is of no consequence. The ONLY interest that Mexico has is that [if upheld] we will be sending back Mexican citizens and they will AGAIN be a drain on Mexico's resources ...
Given that Mexico has tacitly encouraged its citizens to leave for the United States [and thus lessen the financial burden on Mexico], Mexico has NO VALID STANDING in this case ...
No one said they had standing. That’s the point of amicus briefs - they are merely submitted by entities who [think they] are being helpful - not by parties to the case. Parties to the case can submit pleadings, they don’t need to ask permission to submit a brief.