The red light is good. Too much heat can cause pecking. Too little room can contribute, but with only two, that should not be a problem. Too little food, especially protein, might contribute, but it doesn't sound like it as young as they are. Boredom? Could be. You might try a small plush toy or something they could climb or jump on, or especially something they could hide behind. That might give the cochin a place to get away. I think it is too early for treats.
Do you have enough room so they can get away from the heat if it is too hot. Maybe put up a shield (non-flammable) to give them a slightly cooler place to go. The recommended temperatures are guidelines and don't have to be followed exactly all over the brooder. Some chicks like it just a tad warmer or cooler. That's why the starting temperatures are 90 to 95, not a hard, fast set number.
If the heat is right, my guess is that you have Atilla the Ameraucana. Some chicks are just aggressive. I read of someone curing an aggressive chick by putting it in chicky prison (consider it protective custody if you don't like the term prison). Separate it from the other chick but in the same brooder with food and water and a barrier they can see each other through but can't get at each other. Maybe some type of wire basket turned over or a piece of hardware cloth. They will probably protest severely about being apart. In a couple of days, let them back together. This supposedly worked with one chick in a brooder full. I don't know how it would work with two chicks.
Another much sadder possibility is that chickens seem to sense when a chick is too ill or weak to survive and will peck it to death. I'd certainly try everything else, especially separation, before I gave in to this theory.
Good luck.
