*Becomes pale, develops a corpse-like stink and/or requests to have "whichever rations taste most like brains."
*Turtlenecks, scarves or comically oversized watches are usually a bad sign.
*Claims to "really understand how zombies think. Like, really."
*Offers you admittance to the "Blood Brothers For Life No Shooting Each Other" club they just formed.
*You just saw them have sex with a zombie.
Chances of Survival:
Assuming you don't consider the shambling undead "survivors," nil. Unless the antidote/serum/Z-ray is discovered in the next 24 hours, they've basically bought it. The real question in the betrayer's case is how long they can last. If they're a beloved family member, they'll probably make it right up to the point where shooting them in the face will be most fraught with poignancy. If they're a mysterious drifter who just joined the team, they'll be biting bullet before the end of this reel.