Help 2010 Mazda CX-9 towing wiring harness

So having a little bit of an issue. I have a 2010 cx-9 Touring without towing package. When I bought it the nice thing was it already had a trailer hitch on it but I couldn't find the trailer wiring so I'm looking at adding it. Now I looked at one and f the treads here that showed how to install the main harness wiring the one from the back to the trailer. My issue is I don't have the connector at the back so I found the correct part number for the main wire that runs to the front which was 0000-8e-n04 and I have to pick up the one that runs from the back to the front that part number was 0000-8e-n13a which had become a little harder to find from anyone but a dealership. Now part number 0000-8e-n13b the one for the 3500 lb towing capacity is easy to find and looks identical to the n13a. Can anyone tell me if there is a difference between the two of them cause I would much rather get it from eBay or amazon then the dealer cause of cost. I'm going to attach the links and pictures below in case anyone can help.

0000-8e-n04

https://www.ebay.com (commissions earned)

0000-8e-n13a

https://www.ebay.com (commissions earned)

0000-8e-n13b


Genuine Mazda Accessories 0000-8E-N13B Class II Trailer Hitch https://www.amazon.com/dp/ (commissions earned)