I have a personal little AU where Equius and Terezi work part-time as mall cops (officially-unofficially). Equius’s father is a retired cop, and Terezi’s mom used to be his partner, so the two know each other well. 

Terezi rides around on a segway even though it’s slow as shit and Equius usually has to be the one to confront troublemakers while she shouts support in the background.