My security light continues to blink after car is turned off?

This might be normal. can I ask if the car starts and runs and if so does the security light go out after is is running? Please let me know.

Yes it does start and run. The light goes out after starting.

Yep, that is normal the light is doing what it is designed to do. Maybe you can try resetting the system by following this guide to see if the behavior changes:

https://www.2carpros.com/articles/how-to-reset-a-security-system

Please run down this guide and report back.