Welp, totally missed it because vacations. Caster is kind of a curious case here, because he is mostly involved by proxy. Archer uses his name to open doors and get information, but the truth is Archer and Ginia are doing the bulk of the legwork and he's the "independent consultant". He was also present on Zelda's council if Amaterasu ever got wind of that.

Caster would most likely consult some of the shinki about mechanics in the ofuda spells, and if asked why, he wouldn't hide he's investigating the spells left around the forest and the shrines

He's putting his nose here and there, but trying to keep it low at the same time. But while he is not readily and openly telling about his involvement in the investigation, he would answer honestly if asked directly. He also went to Ireland in part to continue the research into cult activity and their relation to gods.