The “hat light” doesn’t have a taper, though. It’s straight, all the way until it hits the curve into the flange. I’m fairly sure if you were shoving the light through a hole in the wand, given how thin the walls are on the wands, you’d see a bit more of it sticking up than is visible there. As for the “metal ring”, it’s a rather yellow-tinged ring, that could just as easily be a part of the design of the lamp casing, or, presuming it is metal, could be from the housing of a different light, possibly even manufactured by the same company. I’m fairly sure that the manufacturer of the original part, who’s name escapes me at the moment, made other lights, besides the hat lights. I mean, could it be the hat light? Sure. But it could also be tens of thousands of other styles of lamps or lamp housing, especially if you’re going on the assumption that it was simply shoved through the roof of the wand. Unless you take that specific wand apart, and actually check the guts, there’s no way to know for certain, and it’s just guess work, based solely on purely circumstantial evidence, at best. It having the same diameter, as I said, doesn’t make it the same part.
As for the internal bits, all I can see in the photos are either an off-white cap, or much blackness. Not much to go on for identifying inards.
I can see where you might think it’s the same light, but I just don’t see it. But, as I said, it really doesn’t matter, anyway, since, personally, I wouldn’t want to waste the money on a casting of it, or even the light itself, to just shove it through the bottom of the thrower. And I can’t imagine anyone else would, either, accurate or otherwise. Especially since it wouldn’t even light correctly unless you got the ORIGINAL part, which would cost way too much and be way too hard to find, to relegate to such a placement.
Chris