led droop chart
That 22 ga. wire can conduct 1A well, you should not worry about that.
But, as you already mentioned, the problem will come from voltage drop on the wire, not the current conducting capability itself. This wire has 16 ohm per 1000 ft., means a voltage drop would be 16V if you use the above diagram with 1A. It is big compared with 12V power supply.
The more commonly used diagram for your lamp/LED "chain" is connecting LEDs in series, not in parallel as you are talking about.
Say, each side of the road, you will connect 25 (500/20) LEDs in series (with the voltage requirement of 25 x 3.5V = 87.5V) and with a resistor of only 1W dissipation (for the remained 32.5V) and directly to 120V photocell. Using this way, you will use only 1 wire each side (not a pair, so you save 1 wire), the voltage drop on the wire is very small either (8 ohm x 20mA = 0.16V), and you will also save the power, and need no 120V-12V transformer.
On the other hand, connecting LEDs in series make them light equally from LED to LED, as they all light by the same current.
Hope this will help.
nguyennam