I'd guess the blinker fluid is low.
One of my friends has a 94 that is turning over, but not starting. He drove it the last few days fine. It might be turing over a little fast.
It did get hot last week, but he said he got it shut down quickly and and it has been normal since. It was a slow leak in the lower hose and was a little low on water/antifreeze.
I am guessing timing belt. Whats the quick test? Any other help would be appreciated. Thanks!
I'd guess the blinker fluid is low.
A compression test would tell you if the timing belt is broke, or you could pull the valve cover and check that way.
If the belt is busted it will sound "different" when it turns over. You can peek down the oil fill while turning it over to see if the cam is moving.
Since it is OBD1 have him check the codes.
http://www.miata.net/garage/faultcodes.html