How to Make Your Thumb Independent
In fingerstyle, the thumb usually holds a steady, independent rhythmic pulse - the bass - while the other fingers play a melody on top of it. As long as the thumb keeps 'adjusting' to match the other fingers instead of running its own rhythm, that independence doesn't exist yet.
Why the thumb usually drifts
The brain tends to sync all the fingers of one hand into a single shared rhythm - that's convenient for strumming a chord, but it's exactly what stops the thumb from holding an independent pulse separate from what the other fingers are playing. Thumb independence is literally overriding that natural tendency to synchronize.
Off-guitar drill: two different rhythms, two hands
Before carrying this over to guitar, it helps to drill the underlying skill on its own: one hand taps an even pulse (on a table, at regular intervals), while the other plays a more complex, irregular pattern at the same time. That exact skill - holding one steady rhythm regardless of what the other hand is doing - is the foundation of thumb independence.
Start with a bass pulse alone, no melody
On guitar, start with the thumb playing a steady, repeating bass pattern entirely on its own, with no melody on top - take it to automatic under a metronome. Only once the thumb can hold that pulse with no conscious control should you add a melody with the other fingers.
Add the melody in tiny pieces
Add just one melody note on top of the already-automatic bass pulse and check whether the bass drifted - if it did, go back to the bass alone and repeat. Build up the melody one note at a time, not a whole phrase at once, otherwise it's unclear exactly when the bass lost its independence.
How to check the independence is real
Play the bass and melody, then deliberately throw off the melody's accent (play it slightly differently, with a syncopation) - if the bass keeps going evenly regardless of what happens in the melody, the independence is genuinely there. If the bass 'stumbles' along with the melody's change, the hands are still synced out of old habit.
Try it in practice
Open the metronome