Yes, in this sense it is countable. 'A light' is a normal expression. In most rooms, there is 'a light' hanging from the ceiling. This refers to a single electrical installation, composed of a light fitting, an electric bulb ,and so on. 'A light' can also refer to a desk light or a bedside light in a room. 'A light' can also refer to a lamp, or a torch/flashlight.

I hope this won't confuse you. "Light" can be an uncountable noun for visible radiation itself, and it can ALSO be a countable noun for SOURCES of light. So all of the following sentences would be correct. "I thought there was somebody in the house because there was a light on inside." "I thought there was somebody in the house because the lights were on." "I thought there was somebody in the house because was light coming from an upstairs window." "I thought there was somebody in the house because it was blazing with light." "I thought there was somebody in the house because it was all lit up." "I thought there was somebody in the house because the front door light was on, and I could see flickering bluish light from a TV set coming through a window." "I need some light over here, can you bring me the flashlight from the desk drawer?"

It might help you to think of it as "an artifical light source", that is what is meant by it. And light sources can be lamps, fires, candles, light bulbs, etc... People may also say there are lights on, if there is more than one source of light.

Yes, in a house you could have many lights. In this case light could be a bulb, a lamp, a flaming brand, a candle or a torch. Who knows? But I don't get it, could you explain TO me why IT is necessary to write "a". Is the word "light" countable?