What you have is a residential elevator made by WheelOvater for Dover Elevator.
WOV was purchased by TKE Access and is now out of business. There is a company in Huntsville called Homelift. They used to be a WOV dealer and are familiar with your elevator. Their phone number is (877) 643-6210. I seriously doubt that the gate switch needs to be replaced, however, it is a possibility. They used GAL gate switches and they are fairly bulletproof in these installations. If the DC module has the indicator lit, most of your safety circuit is Okay. The problem is that GL module is not active and that could be the stop switch inside the elevator or the gate switch. I would suggest that you call Homelift and have them bring along a gate switch and come fix your elevator.