Single-family home in coastal California (3C)(95062) built in 1960 at 1263SF. 

Our walls are currently uninsulated 2x4s. After some exploration, I’ve found our sheathing appears to be some type of 5/8″ gypsum board with black paper (I assume asphalt). This is followed by wire mesh and stucco. 

I had originally thought the house had no sheathing and had taken plans to mitigate moisture problems as described here: https://www.greenbuildingadvisor.com/article/insulating-walls-in-an-old-house-with-no-sheathing

I’m relieved to see some type of sheathing, but still concerned about moisture. 

Will I be ok to simply install batt insulation here against the sheathing? I plan to use mineral wool. Aside from the R-value, I’m hoping this will mitigate any moisture issues since it is hydrophobic (although I’m not sure that scientifically checks out). Any other items I can do to sleep at night? Should I caulk the seams in sheathing?

Thanks.