The harness you found is the correct one, thank you for sending that picture, that eliminates all guesswork.
You can use the Curt T-Connector Vehicle Wiring Harness with 4-Pole Flat Trailer Connector # 56087 on your 2011 Suzuki Equator without a tow package. The wiring is available on all model vehicles.
I attached installation instructions for this product that you should check out also. view full answer...
The CURT Custom Fit Trailer Wiring Harness, item # 56087, does not require the factory tow package for installation. This harness plugs inline with the existing tail light wiring harness on the vehicle. I have provided a link to instructions for you to review.
If your vehicle does have the factory tow package wiring, then you could use the Replacement OEM Tow Package Wiring Harness, item # 118263, on your vehicle. I have linked instructions for this harness also. view full answer...
If you look at the instructions, linked for you, for the CURT Wiring Harness, # 56087, they have attached the converter box to the frame rail on the 2011 Suzuki Equator.
You will want to make sure the frame rail and converter are clean by using a 50/50 alcohol and water mixture. Let them dry before securing the converter to the frame with the included sticky tape.
You can use a Mounting Bracket 4-Pole Flat, # 18144, with # C57202 or # 18140 to secure the 4-Way plug. I have included a... view full answer...