The small halogen lamp is a meant to operate for the period while the Metal Halide lamp is warming up.
That way you will instantly have some light when the fixture is switched on. It is called a "restrike" bulb.
The timer relay which operates that bulb should drop out when the main (MH)lamp reaches full brilliance.

Generally the relay is tapped off of the 120V lead and the common of a multitap ballast.