This really is (or can be) a case where it is up to the GM to make a ruling, and then live with the consequences. Several different effects can be achieved by assuming different features of the invisibility effect.
For demonstration consider particular case: the bard carrying the light emitting item gets turned invisible; the "victim" is in the same room with them. There are no other sources of light in that room, so the room would be dark but for the invisible light source.
Light Remains Visible
I can see cases where it would be cool/sensible to say: the light remains visible, and thus there would be disembodied lights running around (I'm thinking of a setting where there are fairies or other fanciful magic). I also agree with Rouby that referring to earlier versions of the rules is a reasonable basis for making this call in 5e. In the test case, the victim would be able to easily locate the bard, even if he/she couldn't make out his body. The analogy I have in mind is being in a dark room with someone holding a flashlight -- you can see the light, even if you can't see that person's body.
Maybe there are light sources that would only provide a more general sense of where the bard is, but I can't think of anything that wouldn't allow the victim to precisely locate the bard. Combat bonuses would apply if an engagement occurred, but the bard wouldn't be able to just hide, unless he/she extinguished the light source.
Light Goes Away
If you interpret the invisiblity effect as one of transmutation or as a physical illusion — i.e. you've changed the characteristics of the stuff or manipulated light itself, then I'd agree with Dronz's answer: the light goes away. In the test case, both the invisible person and the victim would be thrown into complete darkness, and (obviously) not be able to locate each other at all via sight.
If you interpret the invisibility as a mind-control illusion, i.e phantasm, then I think that you could have the situation where: the light does not go away, so the victim (and the bard) could still see around the room, but have no idea where the light is coming from, and not be able to locate the invisible bard at all by sight. This would provide the victim with the means to know that something is afoot, but the mind control would prevent him/her from having any way of visually locating the source of the light. This interpretation could also apply if you though the underlying effect was an enchantment of the victim.
So, there are ways to rationalize several different effects depending on how magic is assumed to work in the setting. Picking one, and then sticking to it, seems useful in terms of game play, but in a setting where you wanted to emphasize that different schools (or flavors) of magic are really different, you could have different casters have different effects in these regards.