This question came up during a Labrynth Lord game: What happens when a magic-user conjures up an illusionary basilisk to attack another illusionary basilisk? The magic-user did not know that the first basilisk was an illusion and was just trying something to keep the thing busy for a bit.
First off, the illusion would not have any of the Extraordinary or Supernatural abilities of the base creature.
Second, an illusion is under the control of the caster, so it depends entirely upon if the casters think the illusion is, in fact, an illusion. It appears the caster of the second illusion has not successfully identified the first basilisk as an illusion, based upon what you stated, so it depends on if the first caster of the original illusion basilisk can identify the nature of the second one.
If the caster of the first basilisk sees the second caster magically create a second basilisk, did the first caster succeed on a spellcraft check to identify that the second caster was casting an illusion as opposed to a summon? Does the first caster, even if failing to identify the casting, recognize the second basilisk as an illusion?
The first caster should be able to make a spellcraft check and a will save. If he succeeds on either of these things, he knows the second basilisk is an illusion and therefore can choose to do whatever he wants, which is most likely to ignore it.
If he does not recognize that the second basilisk is an illusion, he'd likey assume the second caster summoned an actual creature and interact accordingly, most likely interact with it.
Third, based upon the first point that neither illusion would have the petrifying gaze attack, everybody should likely catch on real quick that there is something fishy going on, since nothing is turning to stone.