Never mind, I googled a bit more and found the answer. For those that might be searching I found this on miata.net
* Question: When the clutch is out, there is a small but noticeable high pitched continuous squeak. This is true whether I am in gear or just sitting in neutral. The interesting part is, if I depress the clutch 1/4", just a tiny bit of pressure, the squeak goes away! Is something awful about to happen? Am I going to be shot thru the *** with bits of clutch shrapnel?
You might try putting a little grease on the end of the push-rod that moves a lever to your clutch-plate. Put your Miata on jacks, get under the transmission/clutch, and have someone push the clutch pedal in and out. You'll see the rod and lever move. Smear a little lithium-based grease around the point where they contact each other.
Yes, but the quick fix is not permanent. Mine is no longer able to be quieted that way, although it does take the worst of it away and no longer sets my teeth on edge. When the noise came back after the "quick fix" had been applied to mine, I tried lubricating it again.
No lubricant I could find worked at all, until I asked the dealer - they suggested motorcycle chain lube. I tried that and it did make a difference. It stays in place much better than other lubricants. The problem apparently is not just the end of the clutch slave rod, but the clutch actuating arm itself eventually starts to squeak on its pivot. The dealer knew of no permanent fix.
It may be the throwout bearing. Try A1, if the noise continues check the throwout bearing. Note that removal of the tranny is required to change the bearing. If this is necessary it is wise to inspect the clutch, pilot bearing, and rear main engine seal.