TOKYO, Sept 14 (Reuters) - Yields on benchmark 10-year Japanese government bonds (JGBs) were unchanged on Tuesday amid a rally in domestic equities that also countered positive results from the finance ministry’s liquidity-enhancing bond auction. The 10-year JGB yield was flat at 0.040%, while 10-year JGB futures fell 0.05 point to 151.74, with a trading volume of 16,754 lots. Japan’s Nikkei ended at a more than 31-year high, led by cyclical stocks while progress in domestic vaccine rollouts raised hopes for an economic reopening.The rally weighed on fixed income investor sentiment even as the auction for notes with maturities between five to 15.5 years had a positive outcome. The auction received bids worth 4.24 times the amount sold, higher than a ratio of 3.1 times at the previous auction. The 20-year JGB yield fell one basis point to 0.415%, while the 30-year JGB yield declined one basis point to 0.640%.The two-year JGB yield was flat at minus 0.130% and the five-year bond yield stayed at minus 0.105% as the bonds were untraded. The 40-year JGB yield was also unchanged at 0.725%. (Reporting by Tokyo markets team; editing by Uttaresh.V)