BERLIN—The mood among German consumers brightened unexpectedly heading into October to reach its highest level in a year and a half, a survey showed on Tuesday, in a sign that households continue to support the recovery in Europe’s largest economy. The GfK institute said its consumer sentiment index, based on a survey of around 2,000 Germans, rose to 0.3 points for October, from a revised—1.1 points a month earlier. The reading compared with a Reuters forecast for—1.6. Both economic and income expectations improved significantly while the propensity to buy rose slightly, GfK said. Consumers became more optimistic in light of falling coronavirus infections that the fourth wave in the pandemic could be less pronounced than many feared, the survey showed. “That is why many consumers can once again see scope for restrictions to be eased further,” GfK consumer expert Rolf Buerkl said in a statement. But Buerkl cautioned that even …