Okay, so you aren't into flatpicks, good for you :) You have a fairly solid background in Classical style, even better! You need to learn and master the following riff, an arrangement by Tommy Emmanuel from the Beatles song "Day Tripper". Use right hand index and middle fingers on the top two strings, the thumb does all the bass line work. If you don't yet have thumb independence then it will take you many hours over a few days to master - how can two bars be so hard? - you are about to make your brain work in a different way. If you master it, then you don't need to read the rest of this blog, you will _understand_ thumb independence.
|-0---0---0---0---|-0---0----0----0---| |-3---3---3---3---|-3---3----3----3---| |-----------------|-------------------| |-------------2p0-|-------4-------0h2-| |-----------2-----|-----2-------2-----| |-0-----3h4-------|-------------------|
Look; just the same as there is not really such a thing as muscle memory there is also not _really_ such a thing as thumb independence. All you are doing is expanding your rhythm from a very basic one to more of a more complex polyrhythm style.
Normally as a classical player your thumb might play the first note in the bar and your fingers will then arpeggio or pattern pluck the rest of the bar, repeating for the next bar in a different chord. Maybe there will be a second bass note, but essentially it is all on a regular beat. It is when you thumb a bass note on an off beat you are performing "thumb independence".
Okay, I admit, true thumb independence _may_ exist. As in, your thumb is doing something completely separate to your fingers. An example would be playing the melody to Baa Baa Black Sheep with your fingers on the treble strings while thumbing the bassline of Peter Gunn at the same time. Well no, that isn't really thumb independence you could train yourself to line up beats. But if you played it through once; and then played it a second time but played the bassline *slower* than the melody - in fact you could play either the bassline or the treble at any speed relative to each other, chop and change sections out at will, then hallelujah, true thumb independence does exist and I will eat this blog.
Meantime, "thumb independence" will completely revolutionalise what you play and how you play, you just won't understand until you understand...understand? This "thumb independence" I talk of is a learned polyrhythm; for example once you have mastered the above riff you now have a tool in your kit where you can strike an off beat bass note in a very specific situation. Continue to learn more songs of that style and the more learned thumb independence patterns you will achieve.
Also - don't just consider thumb independence to be about the thumb, indeed the thumb might be playing a totally on beat pattern, your fingers may be playing the off beat! Thumb independence simply means that what is happening on your fingers and thumb doesn't line up on a "normal" beat.
My continuing strategy for achieving thumb independence is to very slowly bash into my brain a particularly tricky pattern, playing at ultra-slow tempo or even no-tempo, and force my fingers to learn the muscle memory required to perform the pattern. Over time it will sink in and yet another thumb independence pattern is available in my toolkit. It is very forced, difficult and almost unnatural; your thumb will tend to want to pick up on "normal" beats - indeed, it will fight with you. Win the fight; and transform your sound from a very primitive western style rhythm to a creative and interesting polyrhythm!