You go there for work, 3 days a week by commuting e.g. by train.
I meant, why should he be commuting if there's already a director in Zug? Are you suggesting that the company should hire him so he can pay himself a salary and commute few times a week to Zug to justify the salary? It's a 1h.30m ride from Lugano to Zug, so it's not far but neither around the corner. If nobody will check his presence in Zug then it could be worth it.
Zug, where dividend tax is enormous.
If you think dividend tax in Zug is enormous you should avoid Switzerland altogether.