If you throw a red shell while in first place, who will it try to hit? It does try to hit whoever is a place above you, but if nobody is above you, what does it do?
If you throw a red shell forwards while in first place, it follows the track for a little bit but does not home in on any player.
If you throw a red shell backwards while in first place, it acts exactly like a green shell does when thrown back, traveling in a straight line.
If you have a red shell while in first place, it's best to keep it trailing behind you to block red shells and to deter any opponents from passing you.