It is possible to level the total station using the vertical angle if it is equipped with a compensator. What you need to do is set the vertical angle to 90. Now just turn the gun 180 degrees around. It should be 90 as well but most likely won’t be. Adjust your foot screws until you split the difference that it was from being 90. Do this again perpendicular to this line. This is the most accurate way to level your total station. Once you do this you should then be able to spin the gun freely and it should stay at the same vertical angle.
If you don’t use this method to level the total station you will notice that as you spin the instrument horizontally the vertical angle will change. This is due to the spin axis not coinciding with a plumb line through the centre of the instrument.