What are extremal Kerr Killing vectors up to?

In the extremal Kerr spacetime the horizon Killing vector field is null on a timelike hypersurface crossing the horizon at a fixed latitude, and spacelike on both sides of the horizon in the equatorial plane. We explain in some detail how this behaviour is consistent with the existence of timelike Killing vectors everywhere off the horizon, and how it arises in a limit from the Kerr spacetime where there is a similar hypersurface strictly outside the horizon.