I don't even understand your reply. What the hell are you talking about. First you say wire it up to both sources without a relay and now you are asking how a relay works? Are you seriously a mechanic, or are you just messing with everyone?
Let me break this down as simple as possible for you.
Option A (your suggestion)
Run a 12V hot lead from the reverse lights (either taillight or trailer plug)
Run a second 12V hot lead from the up fitter switch
Tie both into the positive side of the S2
Ground the negative appropriately (I assume at this point, but there's no telling with you)
Option B (my suggestion -also supported by anyone who knows anything about 12VDC)
Run a 12V hot lead from the reverse lights (either taillight or trailer plug)
Tie that to pin 87a on the relay
Run a second 12V hot lead from the up fitter switch
Tie that into pin 86 on the relay
Run a 12V fused hot lead from the battery
Tie that into pin 87 on the relay
Tie S2 positive into pin 30 on the relay
Ground the S2 negative and pin 85 on the relay appropriately
Since you don't seem to understand relays:
Pins 85(-) and 86(+)power an electromagnet.
The opens the switch when 12VDC+ is applied to pin 86(+).
It closes the switch when 12VDC+ is removed.
In the closed position 12VDC+ (if present because the truck is in reverse) can flow between pin 87 and pin 30 (powering the S2)
In the open position 12VDC+ (from the fused power source) can flow between pin 87a and pin 30 (powering the S2)
Now, please tell me why your solution is the correct one (even though it disregards basic 12VDC circuitry logic).