MD80 FLC HAS TFC CONFLICT CLBING OUT OF SJC.

Narrative

SJC8 DEP. 3 HRS PRIOR TO SUNSET; VISIBILITY MORE THAN 10 MI; SKY CLR. LEVEL AT 5000 FT; ACCELERATING FROM 230-250 KTS; AUTOTHROTTLES ON/SPD SELECT 250 KTS; AUTOPLT NOT ENGAGED. WE RECEIVED CLRNC TO CLB; WITH A TA INCLUDED. CLB PWR REMAINED SET AS I INITIATED THE CLB; INCREASING THE RATE TO 3000 FPM. DEP CTL RPTS TFC AT 12 O'CLOCK POS; AND RPTS THAT THE TFC HAS US IN SIGHT. WE ARE LOOKING BUT DO NOT SEE THE TFC. THE VVI; VERTICAL VELOCITY INDICATOR; LIGHTS UP WITH MOSTLY RED LIGHTS; WITH ONLY GREEN LIGHTS AT 5000 FT DOWN. NO AUDIO OR AURAL WARNING. TCASII SCREEN IS ON 10 MI RANGE AND SHOWS A TARGET IN RED +200 FT VERY NEAR THE CTR OF THE SCOPE; JUST TO THE L OF THE NOSE; ABOUT 1/8 OF AN INCH ON THE SCREEN. BY THIS TIME I HAVE DISENGAGED THE AUTOTHROTTLE; AND HAVE PULLED THE PWR BACK BUT BEFORE I HAVE IT ALL THE WAY TO IDLE; I LOOK BACK AT THE SCREEN AND SEE THE VVI INDICATES GREEN ONLY NEAR THE TOP 5000 FT UP AND THE REST OF THE VVI IS RED LIGHTS. THE FO CONTINUES TO LOOK OUT THE WINDOW; I AM IN AND OUT; BUT I DETERMINE WE ARE CLR OF THE TFC AND CONTINUE THE CLB. BY NOW WE ARE PASSING 6300 FT. NEITHER OF US IN THE AIRLINER EVER SAW THE TFC.