More info on this odd issue:
I’m creating my game’s main menu; in it, I start with one player, but create players at a certain point along the UI’s flow.
If I launch the game, and just use the player 1 gamepad to control the UI, when I get to the point of other players being created, only player 1 receives input from their gamepad. No other players receive input. This is just like before.
However, if I click the mouse, even before any additional players are created, when the other players are created they do receive input from their gamepads.
And, if I then load another map, players on the newly loaded map (which in the interim the players have been destroyed in the previous map, and then created again in the new map) are still receiving input from their gamepads.
In light of this, I have a workaround; I’m going to force players to left-click their mouse in order to get past the first screen in the menu UI. That way players should correctly receive input from their gamepads.