The white coating on both ends is typically universal burning . Here in the U.S. A base up only lamp has the coating only on the base end while on a base down only version it's only on the crown end of the arc-tube .
I think you have that inverted, a position redistricted metal halide lamp will *generally* (but not always looking at you GE Halarc!) have its white coated arc tube end at the lowest point in the lamp
for example note in the Lamp from Max that I Linked to,
https://www.lighting-gallery.net/gallery/displayimage.php?pos=-154383its burning position is base up only, and notice how the white part of the arc tube is in the crown end of the lamp, as when the lamp is base up that is the lowest point in the lamp
and conversely on this base down burning lamp
https://www.lighting-gallery.net/gallery/displayimage.php?pos=-230971note how the white part of the arc tube is now near the base of the lamp since when burning base down, that is the lowest point of the arc tube
the whole point of the coating is to raise the temperature of the coldest part of the arc tube and ensure thermal uniformity of the arc tube for most optimal performance, and to simplify it, as most of us know heat rises, so thus the lowest part of the arc tube is what needs the most insulation
also with regards to the first line, certain lamps for horizontal burning only will still have heat reflective coatings on both ends of the arc tube, just something to be aware of
so the heat reflective coatings of a metal halide arc tube, can give you a good hint as to the burning position of the lamp, but one should still be on their toes about it if that makes sense