Have removed license plate from rear and removed brake light and running light. Left with plastic harness with 2 black wires--1 red wire--1 blue wire--1 purple wire --1 orange wire. But new plate bracket with brake light and running light has only 3 wires black=ground white=running light red=brake light. How to splice into the 6 wires from stock hook up ?

You need to get a wiring diagram for your bike. Then you can figure what goes where. You might have done this before pulling wires!

I would turn on lights and look for voltage with a Test light, Identify it as Tail light, or write all colors down and Function next to it.
Remove lenses from both Old and new lights, will tell a lot of what wires is which. Then you can do continuity checks on all possible wire combinations. Then apply 12 volts to the pairs of wires with continuity and see what does what.
Tail light may get positive from ignition, and ground from brake switch, see if brake switch has 1 wire going to ground, Lot of wires, wonder if there is a low wattage parking light? Led? Good Luck. A Meter will tell all. Will have to press brake switch to determine which wire that is. Found this:

https://www.twistedthrottle.com/blog/?s=brake+lights

Good Luck