A little after 5 p.m. Thursday in midtown Manhattan, with the thermometer reading 101 but the heat of anticipation much higher, two older women from Idaho found some shade next to a Taylor Swift billboard. “We just want to see…something,” said Gigi, on her first trip to New York City. A whole lot of New York’s security apparatus had been deployed to ensure she didn’t. Swift’s rehearsal dinner , per an NYPD memo , was set to start in less than an hour, with an intimate group of about 100 guests . The larger gathering — with a concert that could be released publicly, according to a new report about arena video waivers — happens Friday. But as Gigi, her friend Shelley and Shelley’s carriage-coddled infant granddaughter sweltered on 31st Street, the wheels of wedding-privacy were grinding lustily into action.…