[TheForge] What (square) taper is an outdoor faucet stem?

[Bruce]

I'm hoping to tap this font of knowledge:

The pot-metal handle for an outdoor faucet suffered the zinc pest after 25
years or more and fell apart.  The stem is a square taper, but there's an
annular rim around it (I don't know why and have contemplated cutting it
off) that requires a longer-than-typical square-holed shank on the handle.

I cannot find a replacement.

One old-neighborhood hardware store did sell me a tool for four stem sizes,
but the fit isn't great so I consider this only an interim fix.

So the best fix would be to find a source of such handles, but I won't hold
my breath about that.

Another possibility would be to cast a replacement from aluminum or
bronze.  I can cast aluminum if need be, but it would require considerable
effort for this one little part.  I've never cast yellow metal.  I expect I
could, but don't consider it high on my list.

Yet another possibility would be to forge / fabricate a replacement from
aluminum or preferably copper / bronze.  The concept would be to take a
small yellow metal disk or thick-walled pipe and drive a tapered square
drift into it.  On achieving a fit, I'd fabricate and/or braze that shank
onto a handle.

The catch is that I don't know the taper of the square faucet stem.  If I
can learn that, I can easily make a drift, and the rest is (comparatively)
easy.

Anyone have a clue?  Or know where to find out?

Bruce
NJ