The value of the first four bytes of the TIM2 file is always 0x54494D32 ("TIM2").
TextER allows you to extract TIM2 files from container files, however it does not include the correct file names.
For more details on this program, please visit the Noesis page.
Noesis allows your to convert TIM2 files into many standard image formats. It also includes a batch option.
List of games using the format
The list is not complete! Feel free to add other games that are known to use aforementioned format.