Testosterone, free
testosterone, LH/FSH, IGF-1, AM cortisol, ACTH, TSH, aldosterone, renin, and DHEA sulfate.Vitamin D, Ferritin (iron) and B-12 might be good to check too as they can cause fatigue.
Thyroid is also very complicated and there are many minerals that are needed in very small amounts at certain stages. I don't know all about this though but I think selenium and copper are two of these? Other people in the forum probably know much more about these minerals.