Like Tech said, the gauge of the wire and/or screws makes zero difference in how the spark system behaves. Any gauge, any type of metal (Al, Cu, Fe ...) will work just fine since the resistance is dominated by the resistance of the air gap, which is several orders of magnitude greater than all the other resistances in the circuit combined.
Heck, in a gasoline engine the spark wires are purposely very high resistance (hundreds to thousands of ohms per foot) compared to generic copper wire, which is tens of milliohms per foot.
The connections between wires and electrodes don't have to be all that great either. The wires don't even need to touch the electrodes and it'll still work. Though the gap(s) between wire(s) and electrode(s) has to be figured into your total spark gap.
There are really only a couple design considerations for a spark system;
1. Total voltage of the source and total spark gap distance. Reduce the total spark gap a bit (~20%?) to account for the inconsistency (or inflated claims from the manufacturer) of the spark source. Piezo's don't generate the same voltage every click. Stun guns rarely generate the manufacturer's claimed voltage and their output will also vary from shot to shot.
2. The breakdown voltage of air is a function of the air pressure. Fortunately it's a nice linear relationship. For every increase of 1 ATM in pressure you need to double the voltage or half the total spark gap.
3. The shape of the electrode tips. The sharper the better. The breakdown voltage of air is about 3KV/mm if the electrodes have a large radius of curvature. Between sharp points (i.e., sewing needle sharp) the breakdown voltage drops to about 1KV/mm. With a given spark source you can jump a larger gap (or more gaps) with sharp electrodes than with blunt ones.
4. Sufficient insulation to keep from shorting the spark system to itself (or you
). Typical wire insulation is basically useless at the voltages in a spark system, the wire might as well be bare wire for all the insulation does. To provide sufficient effective
insulation, you need to keep the wires well separated from each other and anything that is conductive. How far is "well separated"? Basically the closest the wires every approach each other should be more than the total spark gap in the system.
Nothing else really matters all that much. The wire type and gauge, the material the electrodes are made of etc., as long as they are metal then they have sufficient conductivity.
EDIT: Really want to know if your spark gaps are working in the buttoned up and fueled gun? Wire the flashtube from a disposable camera or a NE-2 type (neon 120V) indicator light bulb into the spark system. The tube or bulb should be in series with the gap(s). When you click the ignition system the flash tube will show a blue spark inside. A NE-2 Bulb will blink. No spark/blink then there was no spark at the spark gaps. Both types of lights have fairly small breakdown voltages and consumer very little power from the spark circuit. NE-2 bulbs are often used as the power indicator light in older electronics. "Bus strips" with on/off switches and an indicator light generally used NE-2 bulbs. (NE-2 are no longer acceptable for use as indicator lights in safety critical applications because they eventually burn out.)