Both side Brake Light always on even switch off the engine?

It sounds like the BCM has gone out. But to be sure, you can get a CAN scanner (Controller Area Network) which will work on most cars from Amazon.

Here is a video to show you how:

https://youtu.be/u-4syLc-ifQ

and

https://www.2carpros.com/articles/can-scan-controller-area-network-easy

Here is one for about $99.00 if you need it:

https://amzn.to/3ZixY4v

Here is how to change out the BCM, you can get a preprogrammed unit by searching Google or Ebay. Also, I have included the brake light wiring diagrams so you can see how the system works and which fuses to check just in case. Check out the images (below). Please let us know what happens.

Sounds good, a CAN scan should tell us something, please let me know.

The trouble codes you've provided, P062F and P0603, are related to the internal control module of your 2015 Nissan Rogue. These codes generally indicate issues with the vehicle's Engine Control Module (ECM), which is the main computer that manages various functions of the engine and related systems.

Here's a brief explanation of each code:

P062F - Internal Control Module EEPROM: This code indicates that there might be an issue with the EEPROM (Electrically Erasable Programmable Read-Only Memory) of the ECM. The EEPROM is a type of memory that stores critical data and settings for the control module. If there's a problem with the EEPROM, it could lead to incorrect data being stored or read, affecting the performance of the vehicle. This might require the ECM to be reprogrammed or replaced.

P0603 - Internal Control Module Keep Alive Memory: The P0603 code indicates that there's a problem with the Keep Alive Memory (KAM) of the ECM. The KAM is responsible for retaining certain data and settings even when the vehicle's ignition is turned off. If the KAM is malfunctioning, it could lead to the loss of important data, which might result in issues like difficulty starting the vehicle or poor performance. Like P062F, this could also necessitate reprogramming or replacing the ECM.

I would go over all fuses in the vehicle with the systems on.

here is a guide to help:

https://www.2carpros.com/articles/how-to-check-a-car-fuse

If all fuses are good it sounds like the ECM is having a problem, you can get a preprogrammed unit by searching Google or Ebay.

Here is how to change the ECM out. Check out the images (below). Please let us know what happens.