As independently-contracted employees, gig workers disproportionately suffer the consequences of workplace surveillance, which include increased pressures to work, breaches of privacy, and decreased digital autonomy. Despite the negative impacts of workplace surveillance, gig workers lack the tools, strategies, and workplace social support to protect themselves against these harms. Meanwhile, some critical theorists have proposed sousveillance as a potential means of countering such abuses of power, whereby those under surveillance monitor those in positions of authority (e.g., gig workers collect data about requesters/platforms). To understand the benefits of sousveillance systems in the gig economy, we conducted semi-structured interviews and led co-design activities with gig workers. We use "care ethics" as a guiding concept to understand our interview and co-design data, while also focusing on empathic sousveillance technology design recommendations. Through our study, we identify gig workers' attitudes towards and past experiences with sousveillance. We also uncover the type of sousveillance technologies imagined by workers, provide design recommendations, and finish by discussing how to create empowering, empathic spaces on gig platforms.