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Hello and welcome to JustAnswer!
If the tach is falling to zero yet the engine is still turning (albeit not running) then the most likely cause for that would be a bad crankshaft position sensor. The crank sensor is internal to the distributor on this model and tells the engine controller the location and speed of the distributor. If it's signal drops out then you will lose spark and the tach will fall to 0 even though the engine is still turning.
It could also be the engine controller itself going down, in which case I wouldn't expect a fault code to be stored. The first thing I would recommend is checking for codes and it's likely that you'll have a crank sensor code stored.
I'm a full time tech and at work this morning, I'll get back to you as quickly as I can!