So how do you wire it for the color chasing

Hello, there are altogether 5 input cables for the product and external. The Black wire is power wire, hooking up to negative. The other 4 signal wires touch the positive wire to change colors or modes. Video link: https://youtu.be/ruiCvkVXoPA

This is a tailgate strip right ?

Hello, yeah, you could stick it at your tailgate as a tailgate light strip.

Would I connect the red and white wire together for the brakes?

Hi, thanks for your inquiry, you only need to connect the white wire to the positive pole  for the brake. The red wire is the red light chasing flow.

Can I set this to be a strobe light indicator on an independent switch

Hello, if your switch contains some funtion buttons like brake and stop, turn signal, and the switch connects to your power system, you can set the strip to be a strobe light indicator on an independent switch theoretically.