What are the guidelines for appropriate closeness, distance, and conversation with a male cousin?
All of the Halachos and matters of caution regarding Tznius between opposite genders apply to cousins as well. Certainly one should be careful with touching and Yichud scenarios.
Unnecessary lengthy conversations whether in person, over the phone or texting, between relatives, is inappropriate and not tznius in nature.
Obviously, extended family may greet each other and speak to each other in a way of Derech Eretz (basic respect and in a tznius fasion) but it should be limited and primarily in a public setting.
See Pirkei Avos 1:5; Shulchan Aruch Even Haezer Chapter 21.