WDB FLC RESUMED EARLY CLB FROM PRESENT ALT; AFTER DECLINING AND GIVEN HEADING CHANGE OFF COURSE BY ATC; WHEN THEY OBSERVED ANOTHER ACFT TARGET ON TCASII AT THEIR SAME ALT. ATC THEN CONFIRMED THEIR CLB TO THE HIGHER ALT.

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WE WERE LEVEL AT FL350. TAIPEI CTL HAD PREVIOUSLY CLRED US TO FL390 BY 20 NM PRIOR TO PARPA. AT APPROX 70 MI PRIOR TO PARPA; TAIPEI CTL ASKED IF WE COULD CLB TO FL390 NOW. WE ADVISED THAT WE COULD; BUT PREFERRED TO STAY AT FL350 UNTIL NECESSARY TO CLB IN ORDER TO MAKE THE XING RESTR. TAIPEI CTL THEN GAVE US A R TURN TO HEADING 250 DEGS (45 DEGS OFF COURSE). AT THIS TIME WE NOTICED TFC LEVELING AT FL350 AT APPROX OUR 10 O'CLOCK POS; ON TCASII. AFTER SEEING THE TFC ON TCASII LEVEL AT FL350; WE STARTED OUR CLB TO FL390. THEN WE QUESTIONED OURSELVES IF THIS IS WHAT THE CTLR WANTED SINCE HE TURNED US OFF COURSE. WE DECIDED TO STAY AT FL350 UNTIL THE CLRNC WAS CLARIFIED. TAIPEI CTL CONFIRMED OUR CLRNC TO FL390. WE REINITIATED OUR CLB TO FL390. WE DID NOT GET ANY TCASII ALERT AND I DO NOT BELIEVE THERE WAS A LOSS OF SEPARATION. SUPPLEMENTAL INFO FROM ACN 540290: IN RETROSPECT; I BELIEVE WE DID THE RIGHT THINGS. AS WE WERE NEAR A RESTR AREA; AND THE CONFLICTING TFC WAS VERY NEAR THIS AREA; I THINK IT WAS A MIL ACFT THAT BROKE OUT OF HIS PROTECTED AREA.