I'm pretty sure that even if you're greater invisible and cast say, a lightning bolt, while you stay invisible per the spell, that the spells effects are still visible. I can't find a rule citation though, which is what I'm looking for.
Items dropped or put down by an invisible creature become visible; items picked up disappear if tucked into the clothing or pouches worn by the creature. Light, however, never becomes invisible, although a source of light can become so (thus, the effect is that of a light with no visible source). Any part of an item that the subject carries but that extends more than 10 feet from it becomes visible.
My interpretation of the points I've put in bold is this:
Spells that emit light are visible because there is no way to hide it. Lightning, then, would look like it is originating from nowhere; a random spot in the air.
Spells that are immediately "fired" from the caster become visible as they are no longer in contact with him and become "dropped." A flying ball of acid would originate, again, from nowhere.
Spells that extend from the caster, but don't emit light, do not become visible until they are at least 10 feet away from the caster. (Though for the life of me I can't think of an example for this one.)
Items conjured/summoned by the caster are visible until hidden within the casters clothing.
Also of note:
Of course, the subject is not magically silenced, and certain other conditions can render the recipient detectable (such as stepping in a puddle).
So targets can still hear the caster if the spell has a verbal component, and if there are environmental hazards, like rain, certain spells (not to mention the caster) would become easier, if not certain, to detect.
Your intuition is right.
Only stuff that is either part of you and your gear at the time invisibility is cast, or something that you pocket or conceal under invisible clothing, is invisible. Further, any of that stuff that you were originally carrying that became invisible becomes visible if you stick it 10' away from yourself.
Nothing else is invisible.
Since you didn't become invisible while, uh, "holding" lightning, it's not invisible. You also can't exactly hide lightning in your pocket after you cast the lightning bolt.
So, spell effects simply can't be made invisible after the fact, unless you can pocket them, such as in the case of a continual light cast on a rock.
One can still take the "Invisible Spell" metamagic feat (CityScape, p. 61) which makes the effect of a spell invisible (which, given appropriate spell, can scale from simply "nasty" to "absolutely mean and game breaking") for a total price of +0 spell level. That's right, kids, it costs NOTHING besides the feat. There are some spells that will not be fully invisible, and even Detect Magic will reveal the invisible spell, but combining this feat with Greater Invisibility will do some nasty work on anyone unprepared