Not sure if this will help as my son only did it at certain times... but we learned thst they are sometimes sensory seeking when they suck their thumbs, which is what seemed to be the issue with him. I used to just give him a tiny piece of clay to roll, or a paper to tear, or something soft to hold, and once he had some kind of sensory stimulation he forgot all about his thumbsucking.
1st pregnancy - We had a natural birth at home with our midwife. It was a dream come true!
2nd pregnancy - 2012 Miscarriage at 12 weeks (blighted ovum)
3rd pregnancy - 2012 Miscarriage at 7 weeks
4th pregnancy - 2013 Twins Miscarriage at 6 weeks 4 days
My LG really struggled to give up her dummy and did suck her thumb on occasion especially when she stopped using the dummy at around 4 years old. She stopped the thumbsucking about 8 months later.
I really like this article with advise and insight about thumbsucking: