My recommendation is a little more complicated, but in the long-run it would be less prone to problems from weather and to the existing truck wiring. Part of the problem with tapping into an existing light circuit with an additional load is that the newer electrical systems 'sense' when additional resistance has been introduced "added" to an existing circuit... or subtracted from an existing circuit as in a burned-out bulb. That's how the system knows and informs you when you have a bulb "out".
If you are wanting to add any lighting, keep it segregated from the factory wiring. Use the factory wiring only to provide an input to a relay that will then power your add-ons using a separate fused power supply from your battery. That goes for any add-ons, from a few marker lights to driving lights, to a winch, or to an air compressor. All of those could really cause some screw-ups to the factory wiring which is primarily designed to handle only what it was designed for with only a small margin of safety.
Whenever you make wiring connections, use waterproof connectors, solder connections whenever possible, and ALWAYS fuse or circuit-protect your wiring to ensure that you won't 'zap' something.
With regard to this particular question about a power source for the running boards... .
Work under the dash to get your signal power for the relay, and run the power source wire from the battery to the relay and the output wires to the running boards through the grommet (carefully drill a hole) in the front of the cab on the drivers side up near the brake cylinder poke-through. After you put all of your wires through the grommet, seal it back up with black silicone caulk. Then go out to your auto supply store and buy some small diameter split wire-loom and use ny-ties to protect and secure the wires. By the way, for each of your electrical installations, run your own ground... don't depend on the vehicle ground to always be there.
You were probably looking for a quick-and-dirty way to do it, and there are ways to cut corners, but sooner or later it will cause you problems... . you get what you pay for.