The Hopkins Backup Alert, # HM20101VA, is designed to replace a # 3156 bulb and will not replace the # 921 bulb on your 2010 Suzuki Equator.
Instead, I would recommend looking at the Custer Surface Mount Back-Up Alarm, # BK97DB. This alarm can mount to any surface such the frame or bumper and wires into the reverse light circuit on your truck. Once it is wired in it will send a 97 decibel alert when the truck is placed in reverse. view full answer...
We do have a wiring harness designed for your Equator but I spoke with my contact at Curt Manufacturing and found that the custom fit wiring, # 56087, is not recommended for the 2012 Suzuki Equator.
Since your Equator is not equipped with the factory tow package you will need the wiring harness with relays and a 4-Way flat trailer connector, # C56225. This kit will activate the tow package wiring that is present in your vehicle wiring harness.
To install the Curt wiring on your vehicle... view full answer...