I suggest first, just preventing it. Which I know is stating the obvious, sorry. Just put one of them in a pack n play if you can't be there, or take one with you.
It's hard, because you obviously need to leave them alone for a few minutes here and there, and he doesn't always bite, so you can't tell when he's going to bite. You can't watch him every second of every day. But, for this stage, maybe you could set up a really cool play yard for the older brother with great toys that don't come out of his space, and he can only play with them when he's in there. That way, you aren't punishing him, you are just giving him his own space to play with things he can't usually have.
Even if you give him toys that aren't really toys at all. Some pot lids, an empty oatmeal container, and old remote..etc.
Then, I suggest stop "talking" to him about it. It's just the reward. "I make sister cry, mommy and I talk about it". A simple "no bite" is enough. He doesn't need a long explanation, because he isn't listening. He's either trying to ignore you, or basking in the attention. Instead, make a huge point of talking to him about nothing in particular. Set up the coffee table with playdough, and make things...talk to him about what you are making, play rough, do things that are just for him. But, as soon as he bites, the game is over. "No bite! We can't play when you bite".
Toddlers bite for different reasons. They don't have language skills to say "I'm so mad at you". Sometimes they just love the response. It's very powerful. Sometimes, they are frustrated, (that's when a time out can really help, everybody needs a space to chill out, even kids) Sometimes it just feels so good. Ask around, even adults get so excited and overwhelmed they could bite. They don't because they have learned to control the urge. I wonder if that's where the term "I could just eat you up" came from. Only you can tell what he's getting out of biting. It sounds as if he's frustrated...he's doing it when you leave the room, which sounds like he's a little mad at the baby.
Toddlers can't realize it hurts someone else. They don't give a rat's tail if "that hurts the baby", because they are not able to empathize. Only THEY hurt, it can't hurt the baby, because it didn't hurt him. He isn't ready to hear "That hurts baby" or "That makes Mommy sad", he doesn't have those skills yet. Not for several years.
In a few years though, he will be his sister's biggest protector. By the time he's four, NOBODY will be able to mess with his sister.