2nd G String: How you should focus on practicing with you G string

The simple answer is to play the G string over and over.  The way I recommend doing this is via snake exercises, and instead of moving to a higher string or a lower string, stay on the G string.

Another thing you can do is increase the ratio that you play the G string to other strings during snake exercises.  For example, you might play 2 or 3 notes on the G string for every single note you play on the B string, or you might want to skip a string and play 2 or 3 notes on the G string and one note E string.  The possibilities are endless.  You might play 4, 5, 6, 7, or 8 notes on the G string and maybe 1, 2, or 3 notes on a different string or strings.  You might even want to go as high as 64 notes on the G string for every note or two that you play on a different string.