Wow. How can you even have that kind of an SLA? Like what if you happen to be in the shower or in the middle of traffic or if your Internet drops out or something? How do these SLAs work?
Stuff like bathroom visits, showers, etc aren't usually a big deal since 1) we didn't get paged that often (see the SRE Book on proper alerting design) and 2) three minutes is longer than you'd think. Usually plenty of time to "wrap things up" and get back to your laptop.
If your internet dropped out, you'd either switch to tethering, get your secondary to cover while you drove to the office or a coffee shop, or worst case contact your manager to help find emergency coverage.
Normally when I was oncall, I'd be on the couch playing video games or watching a movie with my work laptop nearby and logged into a shell on my work desktop.