I’m going to answer that question by asking a couple myself.
How did the runner get to second base in the first place? Was it via a double, or a single and an error—or a walk to the following batter who is now on first base? Is the guy on second a “bump on a log”—a runner who really isn’t going anywhere—or is he a definite threst to steal and is thinking about trying to steal third? How many outs are there? And most important—is the pitcher just going through the motions, or does he have a good pickoff move a la Andy Pettitte? If this last is true, that runner had better stay put. I remember how a runner would be standing on the base, tapping the bag with his foot, and Andy would get him between taps…and he would do this with a runner on any base.
And it doesn’t matter whether the pitcher is righthanded, lefthanded or a two-headed green Martian. If he’s gonna get you, he’s gonna get you. I would say that the runner’s best bet in that case is to stay where he is and hope for a wild pitch.