J.S.
I did not have twins but my son around the same age as your son would bite his older sister and I. Sometimes he would leave marks on us and as you said he did not seem to do it out of anger. I first noticed that I had a bad habit of nibbling my little one in which I think provoked him to think biting was a way to get attention or show affection. He has no idea how much it hurt. Good news is he will grow out of it no matter what you end up doing. Bad news is if you put him in daycare he will bite the other kids.
Solution: (for our home)
I would tell him he hurt his sister and make him look at the mark he left on her. I demanded that he say he is sorry and give her a kiss. It did not stop the behavior but did make him realize that it was not nice. I then started putting him in timeout for less then a minute. After the time outs started he quickly refrained from biting. Just remember to give him a hug and kiss after time out and remind him that even though he was wrong, you still love him.