FLC OF AN MLG ACR ACFT FAILED TO TURN AFTER TKOF AS CLRED DUE TO NOT RECEIVING THE APPROPRIATE RADIO NAV INDICATION.

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AFTER TKOF (WITHIN FIRST 1/2 OF RWY) ACFT CLBED RAPIDLY. NEITHER FO OR I RECEIVED ANY INDICATION OF MM AURAL OR LIGHT. JUST AS I WAS ABOUT TO ASK HIM TO TURN; WE RECEIVED A TCASII TA 400 ABOVE AND AT OUR 4 O'CLOCK VERY CLOSE. AFTER 5-10 SECONDS THE ALERT DISPLAY JUMPED TO 7 O'CLOCK AND 200 BELOW. IT'S POSSIBLE WE SIMPLY MISSED ANY MM INDICATION WITH THE SIMULTANEOUS TCASII ALERT; BUT IT'S ALSO POSSIBLE OUR ALT MAY HAVE MADE ANY SIGNAL MUCH WEAKER. TWR EVENTUALLY CALLED US TO 50 DEG HDG AS I REALIZED WE SIMPLY HAD TO BE PAST THE MM BY NOW. TCASII SIGNAL ENDED UP JUMPING FROM 4 TO 7 O'CLOCK; TO 10 O'CLOCK TO 2 O'CLOCK AND AROUND AGAIN. BY NOW WE WERE HDG TOWARDS 360 DEGS AND AWAY FROM ARPT. ASIDE FROM TECHNOLOGICAL FIX FOR THE TCASII; OR A DIFFERENT MODE OF ALERT (SUPPRESS TA'S?) BELOW; SAY; 1000 FT AGL. I THINK THE TWR NEEDS TO BE AWARE OF THE POSSIBLE TCASII DISTRS AN AIRCREW MIGHT FACE. I ALSO THINK THE MM IS A POOR SELECTION FOR THE TURN POINT. (PARTLY BECAUSE I DON'T TRUST THE BEACONS ON THE MLG.) A DME TURN POINT WOULD BE GREAT BACKUP; IF NOT A PRIMARY TURNPOINT (USE THE ILS?).