be careful with the 'absent minded practice' route... I can see where it is attractive to just play while watching TV or whatever, but...

because of muscle memory, if you aren't practicing 'correctly', you'll just get better at doing it 'wrong' or badly or whatever.... It can limit you further down the road. I used to sit watching TV with a metronome connected to headphones in one ear, and then practice my alt picking without really thinking about it... It can work, but be aware that you're likely to get better results more quickly if you're fully engaged in what you are doing...

It isn't as much fun having to think about playing, and the ultimate goal is to be able to play without thinking, but you still need to do the ground work in my opinion...