Fair notice:
I'm a 626 owner/driver, not Miata. However, the Miata and 626 use
virtually identical clutch plumbing, differing only in the length of the
hose and exactly where it runs along the firewall. This advice works
perfectly (based on my experience) on the 626, and should work just as
well on the Miata.

Try it as "Spring, finger over "output" hole, pour in brake fluid, add
rubber cup facing spring, etc...", load the reservoir with BF, and use a
screwdriver or chunk of dowel to pump like a madman. At each "push"
stroke, uncover the output hole. Before each "release", seal the output
hole with your finger so it can't suck air instead of drawing fluid from
the reservoir like it should. Repeat until either your arms fall off
(That'll seem like the most likely thing to happen... if it does, put
'em back on and keep at it!) or until every "push" cycle spits an
unbroken stream of BF from the output hole, from "starting to press", to
"bottomed out". Keep the reservoir topped up throughout the process!

Once you're at that point, you'll need something to plug the output
hole. I've fond that a suitably sized short chunk of wooden dowel
"screwed" into the output hole works well. Remount the MC on the car,
and remove the slave - As you know, simple task - two bolts and unscrew
from the line. Open the slave up like you're doing a rebuild, but
instead of rebuilding it, pour it full of brake fluid, THEN reassemble,
doing your best to avoid spilling the contents. Set it aside for the
moment. remove the dowel (or whatever plug was used) from the MC, and
connect the line to it. Repeat the "pump like a madman" process on the
master, only substituting "The other end of the line" anyplace my
instructions say "output hole". A helper is a Good Thing(TM) for this
step.

Once you've got straight fluid coming from the end of the line, cap it
with your thumb, get your helper off the clutch pedal, have him/her hand
you the slave cylinder after filling the opening the line end is going
to go into with brake fluid, then screw the slave onto the line. Now
bolt the slave back to the tranny. From that point, it's just like
bleeding brakes - "pump pump pump hold! Open bleed screw, repeat" until
there's no more air in left in the system. With the "prefill/prebleed"
operation described, that's a very short amount of time, since there's
very little, if any, air in the line when you start.

Due to the way the line is run, clutches are usually a pure pain to try
to bleed unless you've gotten rid of practically all the air before you
begin. Starting from a dead-empty MC attached to a closed system is an
great exercise in futility, since it just squeezes air into the line on
the downstroke, then sucks it back out of the line on the upstroke - you
can sit there literally all day like that and make no visible progress.

My 626 is the same way (using the same clutch MC, line and slave) -
After opening the clutch hydraulics, trying to get a solid fluid column
from master to slave from an "empty" start will take forever, *IF* it
can be accomplished at all before you lose every last trace of anything
resembling patience. Prefilling off the vehicle turns it into "minor
pain in the butt, but doable". Last time, I ended up stripping the
entire system - MC, slave, and lines, off the car, doing the rebuild,
pre-filling, and the entire bleed sequence (with the slave held higher
than the master so that trapped air bubbles could rise up the tubing and
get vented from the slave, rather than returning to the MC to undo all
my progress) and had the bleeding done in about 5 minutes. Put
everything back on the car as a unit (by feeding the slave down amongst
the engine parts to where it belonged on the end of the hose) in about
15 minutes, and the whole job was done, including the rebuilding that
was needed, in less than an hour.

Clearances on the miata may be a bit tighter than on the 626, but I
suspect you'll be able to pull the same stunt, should you so desire.

Jim,

When you say you pumped it 100 times, were you opening and closing the
bleeding screw each time?  Just pumping the pedal without bleeding the
air will do absolutely nothing, not matter how many times you attempt
it.  Clutch systems are a pain to bleed by hand, a mighty vac or similar
vacuum creating system, makes the job much easier but, one way or the
other, you've got to bleed all the air off before it will work and
before you'll see an appreciable drop in the fluid level.

Tom
92 Red (gone but not forgotten)
05 Vette (red, but of course)