multi-meter current reading dropoff
From your question I have the impression that you hooked up the armature to an external source. It also seems that there is a lipo inside the light fixture.

If the above is correct than the behaviour can be explained as follows:

Upon connecting the power supply both the lamp and the battery receive current from the external supply. The lamp is on and the battery starts charging.
When charging progesses the charging current will reduce (simple charging circuit no cc/cv) and the lamp keeps on.

This would explain why the current is high at the beginning drops of slowly. 

The current is therefore in a large extend dependant on the battery charger inside the armature.

To measure the power consuption this way would not be correct. You would have to deduct the stored energy in the battery. Without opening the armature and separating the circuits you are not able to determine how much current is going where and consequently how much power is used for the lamp and the battery.

I looked up the Magicshine and indeed there is a lipo inside.