Tractors generally are equipped with a 7 pin plug not a 7 blade plug that is commonly found on pick up trucks. The 7 pin is commonly seen on semi trucks. Note that the stop and turn signals are separated on a 7 pin but combined on the right and left channel for the 7 blade. Also there is no trailer brakes on the 7 pin.
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Below is the common 7 blade plug. Note the differences in wiring.
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The other end on the 12396410000 kit that OP lists is not a standard 4 pin trailer plug. It is some other plug design. $100 is not a bad price from TYM compared to tracing wire, finding a matching plug to the harness and fabricating the loom. The problem is that
@Balazar will need an adapter if trying to use a 7 prong tractor with a 7 blade trailer.
Below is an example of an adapter.