A nice entry for the game jam! The music is a bit grating in the long run, but the gameplay is nice. I did discover a bug: the player who can hold switches can have its switch activated by the other character and they can sometimes reach the flag by doing this. If the holder has a switch upon reaching the flag, it will still hold it in the next level.
Otherwise, it's a nice idea to expand upon after this game jam. Congrats!