What does it mean when the check engine light goes from on all of the time to constantly flashing. 96 neon

Misfired.

flashing check engine light usually means the engine is miss firing,this can cause damage to the engine and catalitic converter

There is something wrong with your engine. Go to a mechanic to get a diagnostic report.

It means that the comp=ECM has picked up a fault code & has recorded it internally.More then likely it is a fault code dealing with emission devices on the vehicle failing or acting up.Be sure u have a free scan run at a shop or parts store etc to find out what code the main comp=ECM has recorded or stored.

Hope that helps & best of luck.By the way do not panic just find out what the code or codes r on it & always get more then one quote or opinion on such repairs before spending any cash.

you should definitely get it into a mechanic. It is an old car and it is telling to check the engine so check it!!

You could have a bad 02 oxygen sensor that is giving your computer a code that places your check engine light to turn on. Your local advance auto parts store can run a diagnostic check for you for nothing and can tell you what is happening for sure so that you can correct this issue.