The Blue Ox Tail Light Wiring Kit with Block Diode # BX8811 that you referenced does not come with a 4-Way connector as you stated.
To add a 4-Way connector you can simply use the Hopkins Wiring Harness with 4-Pole Flat Trailer Connector # HM38138 and connect it to your current wiring using Butt Connectors # DW05744-5.
For a look that is a little more clean and will provide you with a 7-Way to connect to your RV you can use the Hopkins Nite-Glow Tow Bar Extension Cord w/ Socket - Coiled... view full answer...
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