The 06 Armada and newer that did NOT come with tow package will need the 4th relay.I recently installed a hitch on my 2006 Armada and ran into this same problem. I installed the standard 3 relays, checked the fuses under the hood and looked for the inline fuses under the dash (never found them) but still could not get it working.
Eventually I discovered a connector for a 4th relay under the dash. It is located right next to the connector for the electric brake controller. I plugged in one of the blue relays (the ones for the left and right trailer lights) and now the running lights work. I talked with the guys at Valley who make the trailer connector kit. They never heard of this 4th relay but said they would send me another relay.