I'm starting this thread more for posterity than anything else. I searched all over the place and couldn't get a clear concise answer on how to solve my problem. Here's my story:

I picked up a 95 Miata that had the CEL lit. The code came back 16 which I searched and found that it meant there was a problem in the EGR system. There is a post on Miata.net that steps you through solving the problem on 99 and newer cars with OBDII, but I couldn't get it to work on my car.

Here's how I solved my Code 16:
1.Unplugged (-) cable from battery while working to reset computer.
2.Removed EGR valve by disconnecting vacuum line and wire connector from top. Removed 2 12mm bolts that connect it to the intake manifold - careful not to lose the gasket.
3.Removed the sensor with 3 phillips screws.
4.Found that I had gobs of carbon sludge built up in the valve and that it was stuck open.
5.Cleared as much debris as I could with a screw and CLP that I use to clean my gun. It breaks up the carbon pretty effectively.
6.I had to get a hammer and GENTLY tap the diaphram at from the top to loosen the valve. Once loose I fillled the whole unit with CLP and opened/closed the valve manually several times until it went easily.
7.Cleaned as much more debris that I could
8.Let dry
9.Reinstalled and reattached battery lead.

10 - NO MORE CEL!!!