Pulling/towing a vehicle uses a different wiring scheme than a trailer.
Given the parts you are referencing and the comment on the tow bar -- this is a hardware diode kit. These are NOT inter-changable with a 4 to 7 pin towing system. It would appear you need to rewire.
For a trailer:
typical 4 to 7 pins
ground
running lights
left turn-stop
right turn-stop
power
reverse
brake
For towing a vehicle, there are several solutions:
Lifted from etrailer
https://www.etrailer.com/faq-wiring-kits-for-vehicles-being-towed.aspx#diodeTo legally flat tow your vehicle you must ensure that it is properly wired and connected to your RV. Your towed vehicle's signal lights must act in accordance with the brake and turn signal lights on your RV or tow vehicle. There are four basic ways that you can achieve this:
(1)Removable tail light kit
Bypasses towed car's electrical system
Easily mounts and removes for occasional towing
(2)Bulb and socket kit
Bypasses towed car's electrical system
Permanent solution for frequent towing
(3) Hardwire diode kit
Splices into towed car's wiring
Permanent solution for frequent towing
(4) Custom-fit, plug-in wiring harness
Plugs into towed car's wiring
Permanent solution for frequent towing
Hardwire Diode Kits
Diode Wiring Kit
The traditional method of wiring your towed vehicle to ensure that its signal lights will act in accordance with your RV's lights while it is being towed, is to use a diode kit. This method requires a more involved installation process, but once complete you never have to re-mount, set up or manually activate a thing.
Hardwire diode kits can include:
4 Diodes for 2-wire systems (or for a 3-wire towed car that you intend to wire as a combined system)
6 Diodes for 3-wire systems
Single block-style diode for either 2-wire or 3-wire systems
Kits that include either four or six diodes that splice into your towed car's wiring are the most common tail light wiring kits.
(addition information in the link)