A week’s evidence that the US economy’s ill health has been overstated and dovish talk from the Federal Reserve combined to briefly catapult the S&P 500 Index above its May 2015 record close, leaving stocks on the brink of ending their longest drought of the bull market. Gains on Friday capped an eight-day rebound of 6.5 percent that restored $1.4 trillion of market capitalization to US shares, value that was erased in the aftermath of the UK vote to leave the European Union. The S&P 500 advanced more than 1 percent for the fourth time in two weeks, after stronger June payroll growth calmed concerns sown by May’s anemic number. Banks, technology, and retailer shares were among the biggest contributors to the rally. Starting with a report Wednesday showing service providers expanded in June at the fastest pace in seven months, and continuing with Fed minutes that indicated less urgency in the need to raise interest rates, investors have been treated to enough good news to put the Brexit trauma behind them. Then a report Friday showed America’s job market stirred to life after a two-month lull, as payrolls climbed by the most since October, exceeding the highest estimate in a Bloomberg survey.