Unless someone swapped out your generator/remote panel, there should be a multi-wire run from the remote that plugs into the appropriate harness on the generator.
The hour meter should run off the "running" indicator in the start/stop/prime rocker switch on the remote panel
Onan service manual says time meter defective, not wired would be a defect... Should be a 4 wire harness, see which wire in the harness isn't connected to anything.