Well mostly practice and observation to be honest, all endocrine glands are quite tricky and are under multiple influences imo.
Margaret Miller wrote about thyroid being ruled by Mercury because of closeness with fifth chakra ruled by Mercury and characterized by communication. This even makes sense to me, other places I found it to be connected with the Moon also because thyroid problems are 10 times more likely in females than men(Moon's exaltation in Taurus). Parathyroid(part of thyroid) on the other hand is ruled by Saturn, it is in the same spot at thyroid, in throat - body part that is ruled by Venus, yet it's functioning is connected with calcium distribution and absorption, thus comes Saturn.
I mostly read authors in my native language so not sure other resources would be useful, but just accidentally I do happen to know more than several people with Thyroid disorders and have their charts in my database, mainly hypothyroidism and Hashimotos disease, which is the autoimmune illness of thyroidea, autoimmune would in logic be something showing Uranus effect, no? the simply idea that the entire organ is rebelling and producing it's own antibodies, basically destroying itself, must be some transsaturn influence imo, most closely Uranus, even Pluto when it comes to enlargement.
All in all, I've observed strong Uranus influence:
- Uranus right on the ascendant(three cases)
- Uranus rulling the 6th house(in case of poster above too)
- Uranus hard aspect to lights or 6th house ruler
- also Taurean Suns
- Uranus transits usually marking an onset of illness
are just some of the involvements of Uranus, I've seen it over the years so I instantly associate it with Uranus, although yes I do have read about Venus/Taurus as ruling the part of the body-throat, but to me it needs more than influence of afflicted Venus to make it go out of whack.
Being that all endocrine glands are governed and balanced by pituitary gland, rulership of pituitary is assigned to Uranus, it is a good explanation that sometime the dis-balance in thyroid function stems from something being off in pituitary gland, and that thyroid function is only a side-effect of that.
To each their own, I quess, but practice is what it all comes down to eventually.