WOW!!!. Now I have an answer. I have the same problem with dark patches on the sides of my neck going down to the area of my thyroid. Looks like dirt. All the dermatologists I've seen say its sun damage but my neck is the only place these brown patches are. I tried, for years, different cosmetic procedures to get rid of this, but it always came back. I've spent a couple of thousand dollars. Thinking back now, it started around the time I became hypo. I'd finally come to the conclusion that it was hormonal (perimemo) never thinking it could be thryroid related. Now, maybe, I know different. This makes more sense. It seems like the thyroid plays a bigger picture than we think.
I'm not taking Iodine yet, but it will be interesting to see if it helps lighten it a little.