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...
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...
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...