The specs don’t specify what gauge wire I should be using.
From the video & photos, it seems to be 2 or 3 different-sized wires used to connect the components together.
Can someone with the knowledge suggest the appropriate gauge wiring I should be using?
As a beginner to electronics, due to safety, I will not be connecting this to any electrical power until I have the controller assessed by a licensed electrician.
However, I wish to complete as much of the basic wiring connections myself before I call in the licensed professional.
The main concern should be if the gauge of the wire can tolerate the maximum current that the wire may experience. If you undersize the wire for the load, it can heat up and become a fire hazard. There are a number of wire gauge calculators and tables online to calculate/look up a minimum safe gauge to use depending on the wire and electrical characteristics in your system.
With DC voltage, you also have to worry about the length of the wire causing a voltage drop that may cause issues for whatever device is at the end of the wire. Due to the properties of AC voltage, conductors carrying it don’t typically experience as significant of a voltage drop as DC unless the lengths are incredibly long. The voltage drop for DC isn’t really a problem with short spans inside a control panel, but when you start running sensor signal wires out of the panel, for instance, you may start to experience signal issues.