HPS lamp goes on and off all night long
This looks suspiciously like the documented cycling behavior of a HPS lamp that is near its end of life.  The HPS lamp is similar to a fluorescent, but instead of using a surface-coated phosphor to convert the UV to visible light, it uses sodium mixed in with the mercury.  As a result, the lamp has an internal discharge that is struck upon starting and gives it a negative resistance characteristic, controlled by a ballast (typically an inductor).

When it nears end of life, as in the case of your lamp, reactions with the lamp's alumina (synthetic sapphire, really) shell have depleted much of the sodium from the lamp, raising the voltage required to maintain the discharge to a point where when the lamp is fully hot, the ballast can no longer provide that voltage, causing the lamp to extinguish and re-strike when it cools down.  Newer HPS ballasts have a counter in them that keeps them from sitting there and wearing out the lamp trying to strike it repeatedly -- instead, they will "lock out" the lamp until power is removed/reapplied.

Replacing the lamp should get you another 20,000 hours of light -- unlike with incandescent or compact fluorescent lamps, LED retrofits for HPS aren't nearly as advantageous lifespan-wise, although they exist if you wish to go that route for color rendering or disposal considerations, as HPS lamps have mercury in them and should be disposed of along with their fluorescent counterparts.