He is not involved at all. I mean Belichick is an advisor there too. They have a lot of former NFL/College players and coaches involved in some capacity for some specific items in the Company. I listened to numerous interviews by Spielman and Tanny. For this search it's two of them and that's it.
They are trying to compete with Collinsworth’s Pro Football Focus that provides analysis on player performance. They do a lot more than consulting the NY Jets. it’s likely Adam Gase has absolutely nothing to do with this, especially since he probably doesn’t have much to think of Woody Johnson himself
I am sure Tannabeaum doesn't think that highly of Woody either, the only thing they like about Woody is his money.