It sounds like you're looking for a wiring kit like the 4-Pole Trailer Connector and Installation Kit # C59496. This comes with the 6-wire input and then converts to the 4-wire output like what you mentioned.
The black wire is for 12V battery power and then the red wire is that brake wire. You can just cut and splice this harness in to where your current connections are so you don't have multiple spliced connections. view full answer...
Based on standard trailer wiring colors the white wire will be the ground, the brown would be running light, and the green/yellow will be the stop/turn circuit. view full answer...