OK, was starting a post here, and since I eventually solved it, it became a "note to self".
Lines drawn in Annotate tab, detail, detail lines, are in the view template/ view properties, V/G overrides Model tab, under "Lines".
To me, it's an illogical arrangement, and if I can customize this in some way it would be amazing and instructions very appreciated, but I have a tough time with 2D annotation objects being in a model V/G overide environment. Call me an old CAD dog.
It's listed under the model categories because it also controls model lines. I can see your point, but there would have to be two completely separate sets of line styles (i.e. Thin_model and Thin_annotation) to have them sorted otherwise. And doing that brings up a whole other set of coordination issues (i.e. do you want your Thin_model lines and Thin_annotation lines to be the same weight, etc.).
You're probably fighting an uphill battle on this one, but you could always log it as a feature request.