Upgrade to Smart Switch for a Post Light?
Always use logic to solve electrical problems.  Uninformed trial and error will lead you to many combinations which will "work" but create a lethal condition, either immediately or by breaking the redundancy that keeps electrical safe, so a trivial/routine failure elsewhere that shouldn't create a hazard, now does.  The fact that you are connecting a switch white to a wall black says you should not be making guesses. 

With 3 wires on a dual switch, one wire is "common" to both switches (and is typically supply, so it is always-hot).  This is identifyable from the labeling or obvious connecting metal on the old switch. 

The other two wires are the switched-hots going to one light or another.   

Now, since one of your switches "does nothing", the switched-hot wire associated with that switch can be eliminated.  It should be capped off, on the off-chance it is being backfed somewhere, and so it doesn't accidentally come in contact with a hot screw.   

That leaves 2 wires.  One is always-hot, the other is switched-hot to the lamp. 

However, the fact that the smart switch has a white pigtail tells us important things.  UL forces them to use certain colors for certain things: 


Green, yellow-green or bare for ground
White or gray for neutral


Since the manufacturer could have easily used any wire color, we may infer the green wire MUST be safety ground, and the white wire MUST be neutral.  You must consult the instructions to see if those connections are mandatory. 

Just like pesticide use, use of the equipment according to instructions is mandatory by law. 

Grounds should be connected first, for perception reasons.  In the event of a wiring issue, this makes you focus on the actual wiring problem, instead of erroneously blaming the ground for failing somehow (not likely).  All grounds go together.

Neutrals connect only to that same circuit's neutral, not any other circuits'. This is usually straightforward if neutral is present.  Neutral will be present here.  

Now we have narrowed this down to 2 wires from the wall and 2 wires from the switch.  Since all wires are hot, and the job of a switch is to connect them or not, experimentation is not harmful.  However a simple voltage tester will tell us the hot wire, and the switch's instructions will tell us the hot wire (coughblackcough).