There are no clear stage directions with regard to lighting in the script itself, but one can assume that the bright and jovial mood in the room would definitely be toned down by the arrival of inspector Goole and, as such, the light would also, to reflect this, be turned down a notch. It would, therefore, be practical to dim the lights slightly once the inspector arrives. Even better would be a slight flickering of the lights and maybe a brief haze in the fireplace. This would indicate to the audience the significance of the inspector's arrival and would suggest a supernatural identity.
The slight adjustment to the light on the inspector's arrival would make the audience instantly aware that the he is no ordinary man and would add to the drama. It would also create an eerie atmosphere and ensure greater interest in the events about to unfold. The creation of such a mood would be supported later when the inspector displays his uncanny insight into not only Eva's unnatural death, but also his inexplicable knowledge of the relationships each of the characters had with this unfortunate girl. This awareness by the audience would keep it in greater suspense for it would want to know who or what the inspector actually is and would not betray the plot. An expectation of something would be created and would create deeper intrigue.
This type of lighting change would remind one of the supernatural elements and events present in one's daily life - those inexplicable little occurrences, such as, for example, deja vu, which we cannot always explain. These experiences add to our discomfort and uncertainty and act as a warning, I suppose, that we should not just take anything for granted as the Birlings and Gerald obviously did.