no oil wont cause your tach to bounce around, if the engine has no oil it will just stop and thats no good. Almost sounds like a failed mass air flow sensor. should set a dtc. When the maf stops working the car uses the speed density tables for airflow calculation. These tables arent even close to what they should be for stock and are only used when the maf fails. This will cause the tach to bounce up and down alot and in some cases the car will shut off. First see if it has any codes, if its for the maf you can try cleaning it off. use electronic cleaner and Not brake/carburetor cleaner! You will destroy the sensor!!.... if that doesnt work proly have to replace the sensor.
Good luck
Chris
