Brake bleeder device

Folks--

This is really something I should know and I am a little embarrassed
that I don't. The topic is brake bleeders. Not the fill fitting on
the bottom of the calipers, but rather the device one uses to push
brake fluid uphill into the system (I fill from the bottom up, which
works very well for this plane).

Until recently I used a little squirt gun contraption that several of
us cobbled together. It never worked to full satisfaction but I
grunted through. During the last fill cycle I broke our little squirt
gun and a guy on our field hauled out his own homemade filler to save
the day.

He had a pressure sprayer (the sort of plastic pump-up pressure pot
item that one often sees used to dispense weed killer or pesticides,
etc) with a fitting on the end that attached to the bleeder fitting.
Super simple, super effective.

He has gone to Florida for the winter so A) I can't borrow his any
longer or B) ask him the particulars of his device. So I'm asking
you.

One guy on the field is hypothesizing that the key element of the
device (the fitting that attached to the bleeder valve) is nothing
more than a fitting for a grease gun. This is very plausible but I'm
not sure. The geometry looks pretty close.

Another guy is fairly sure the fitting in question is an Aircraft
Spruce (or Wicks, or WAG Aero) part that is specific for the purpose.
In the Spruce catalog it is P/N 87-5, Cleveland Brake Line Bleeder.
Which of course begs the question of whether or not it is only for
Cleveland fittings. Can't tell from the line drawing. It does not
look the same as the one my guy on the field had.

And yes Spruce also sells the whole assembly in one go but it is
nearly $70 plus shipping, whereas I can get the constituent parts for
less than $15 if the fitting is generic.

So, what's the fitting?

Thanks in advance, and stay safe.

Steve.