For off-hours issues they're the first one called but since it's not an official on call (ie not paid for it and don't carry pager) we're not required to respond. If whomever is on call doesn't respond then the other person gets called (which rarely happens). It works well since we're both dedicated and respond if we can
I had this exact same situation at Citrix where my partner was a 21 year old kid that slept so hard a hand grenade could not wake him up and I got called as his backup all the time so I was doing on-call constantly. Citrix was very political and the boss liked the kid and made every excuse for him like for example "Well Travis he takes prescription medication at night". Well I immediately said "Well boohoo, I have a couple of beers at night does that let me off the hook when I am on call and fall asleep?" Citrix managment is some of the worst I have ever seen in over 28 years in this industry. It's almost fast-food (Burger King) oriented managment, Just terrible. 😀
"Technology is a weird thing. It brings you great gifts with one hand, and it stabs you in the back with the other. ...:-D"