Yes, I've been wondering that as well, though I'm never completely certain until I actually write out what he thinks and does. On one hand Turncloak (who I only now in this writing moment realized was not called Turncoat) pretty much unceremoniously murdered Tomb the moment it showed up, or so Perfect would interpret it, which would not exactly bode well in regards to them being welcoming towards strangers... nor would Turncloak practically assaulting Prince and aggressively interrogating him. On the other hand Turncoat was accommodating enough to instruct Maldron not to attack (though the fact that such an instruction was necessary would be a point against him revealing himself), and Tomb was rather evidently not human, so slaying it might be interpreted as a matter of necessity and/or hostility that would not necessarily encompass humans as well, and it would additionally imply a familiarity with the world that Perfect doesn't have, and the strength needed to dispatch creatures that have departed from the mundane.
So what am I saying, in the end? Perfect might want to reveal himself already, or he may still be too unsure about their group to do so, but considering that they did not outright attack Prince, I'd figure that odds were in favor of the former option. But what would be ideal? A show of obvious hospitality towards Prince would lure him out for sure, or the revelation of resources that Perfect knows he can't do without, such as water. Beyond that, the most surefire - and quickest - way to reveal him would be to have someone notice him. Such as someone conveniently located at higher ground, in position to see over the rocks and weeds he's hiding behind, and spot his large frame lying conspicuously flatly on the ground there. Such as a ways up the walls of the canyon.
He'll definitely be interested in Tomb, though. Heh, maybe his curiosity in that regard would be enough to prompt him to reveal himself. But that's the situation as I'd estimate it at the moment.