As, I hope, you are aware TCAS will react to his non-compliance and adjust the demands on you to avoid the collision. TCAS will also pick up his movement before you could visually. Remember TCAS 'negotiates' escape manoeuvres between conflicting traffic, something you couldn't do.
Of course, but occasionally the RA isn't enough to remove you from the conflict no matter how accurately
you follow it. Ever been pinged by fast jets? Or by a guy who has reacted in the opposite sense(That's the guy I'm on about by the way)?
There was a 'Guy' at my old airline who "was confused by the symbology" and didn't do as he should have. They got within
feet of the other aeroplane who was following his RA but then had to maneuver himself away from the collision, not in contradiction to the RA but laterally at the same time.
Remember I am not advocating not following an RA but when
that isn't enough then your last line of defence is your eyes.