Can you run a wire direct for my rear running lights and dash lights?

You should never connect any accessory directly to the battery in a car. If a short happens, you will have the full current capacity of the battery routing through the passenger compartment. The current capacity of a car battery is enough to melt a solid copper 14 gauge wire in a flash. This can easily start a fire.

If you must, go to an auto parts store and buy an in-line fuse kit. Put a 25 or 30 amp fuse in it and use no smaller than 18 gauge wire in your new circuit.