Red key immobilizer light flashing

Very likely to be the antenna that sends out the signal pulse that triggers the key. They seem to have a high failure rate. It is part of the ignition switch module and needs to be programmed to operate with the parts you currently have. Not a DIY job unless you have the tools to flash the replacement module.

Once the module is replaced a dealer and some locksmiths can program it.

Did you just add any other devices that could be interfering with the signal? Perhaps another Nissan registered key on the same key ring, an automated toll or other type automated payment device in the car?

The module is behind the dash, it contains the key slot the intelligent key is inserted into. That module talks to the instrument cluster and the BCM on the data bus. No activity when the button is pushed, with the security light flashing means the system does not recognize the transponder in the key.
The system works using the module to send out a signal pulse from the module. That pulse is enough to "power" the transponder chip in the key and it returns a signal the module receives and it then compares that information with the stored key information. If the items match the system is commanded to start. If the information is not correct, either through an incorrect key or the signal not working you get the flashing security light.
The first thing to do would be to use a dealer level scan tool to query the immobilizer for any stored codes such as the ones listed in the table attached. Then proceed from there. I would not even start taking thins apart without testing, that module is close to $600.00 so testing first could save a lot of money if it turned out to be a wiring issue or something else.

Not great, just trying to be honest with folks. The alarms and immobilizers in vehicles these days can make even something that used to be a simple thing into a nightmare if you don't have all the correct tools, training/experience and service information.
In some ways the modern electronics make it a bit easier to do diagnostics as they can point to the system the computer sees the wrong information from, in your case the immobilizer codes are related to specific parts and tests but you need a good scan tool and the factory information to run the tests.