The basic idea is that antibodies against self are elaborated to protect the body against gut bacteria that the immune system is getting too good a look at, thanks to a leaky gut. If some of these antibodies cross react with TSH receptors, thyroid activity gets stimulated. This is the case in people, and I've been able to resolve their hyperthyroidism by resolving their leaky gut issues.
Similarly, studies have shown
that antibodies in cats with hyperthyroidism dramatically increase thyroid activity when injected into other animals, proving that feline hyperthyroidism (at least in the initial stages) is caused by antithyroid antibodies. The study cited here is one of the last that was done on the subject and shows how earlier studies claiming this was not the case were flawed in design. This study was ignored unfortunately and the matter has not really been investigated since, but it highlights that tackling hyperthyroidism using this approach should yield some benefits, especially in cases that are not too advanced.
It's no coincidence, then, that the first sign of illness in hyperthyroid cats is chronic vomiting. Addressing gut health and resolving the chronic vomiting tendencies by changing the diet is job 1 in tackling hyperthyroidism from a holistic perspective. I've seen T4 levels drop to normal when IBD and leaky gut causing chronic vomiting in cats is successfully addressed.
Hopefully this helps you out!