"Keep in mind that there are two ground wires going to each headlight and one 12+ which is hot all the time. " This is the OEM configuration.
I suspect a harness from SUVLights.com would plug into a socket removed from one of the headlight bulbs and use the switched ground to complete the circuit through the trigger coils of two relays. I further suspect that there are only two wires in the harness going to this plug. Since nothing has been said about a Sport lamp conversion, the harness sounds like a fairly simple circuit.
I have a little trouble understanding how your lights are now operating. With the headlamp switch (dash) on does the multifunction switch (column) allow you to switch from high to low to high and so on, or does it go from high to OFF to high and so on?
If my assumptions in the second paragraph are correct, and nothing is loose as BGS suggests, the next thing to check is which of the the pins in the plug are wired. A 9004 bulb, used on non-Sport Rams, should have pins B (low beam) and C (high beam) wired. Pin A would not be used. 12 volts should always be present at these pins B & C, and grounding these pins would cause the low or high beam relays in the harness to close.
It is possible that you have a harness for 9007 bulbs. The socket for the 9007 and 9004 bulbs are the same. The socket pin wiring is not. The 9007 socket uses pin A (low beam) and pin C (high beam). Again, if my assumptions in the second paragraph are correct, if pins A & C in the harness plug are wired and pin B isn't, you have a 9007 harness.