Just a bit of clarification. TCAS II interrogates only for Mode C replies. Even if a transponder is not replyiing with mode C altitude, it replies with Mode C timed framing pulses.
TCAS calculations are based on range, closing speed, and altitude difference. Approaching a non altitude reporting target, closing speed is extra important. The closing speed will diminish in proportion to the altitude difference. The non-altitude target will either disappear, or appear to move in an arc around your own plane.
TCAS directional antennas only provide bearings of +/- 15 degree accuracy, and are merely to aid the pilot in looking out the window for the target. There is no bearing accuracy requirement for targets behind.
What gets interesting is when a transponder is reporting erroneous altitude. One time, a KAL 747-2 was squawking 7,000+ feet while really at 10,000, and nearly caused a collision with another TCAS equipped plane.
GB