Your timer assembly is not the 12-day Skipper Wheel timer version shown in R4's link, but instead, as you identified, is an Ecomominder mechanical controller which utilizes a flow meter to initiate tank change and regeneration each time a specific number of gallons (current Capacity setting = 1625 gallons) soft water has exited from the softener. The product number you provided, is the model equipped with a 120 volt timer motor whereas the link below, shows the 24 volt version.
https://www.softenerparts.com/Timer...pm--34-standard-60376-111-24-VOLT_p_2831.html
Both the Fleck 9000 and 9100 valves, utilize identical controllers. The 9000 valve utilizes a brass valve body whereas the newer 9100 is equipped with a Noryl (plastic) valve body. Depending on water conditions, the 9000 brass valves often experience corrosion and pitting on the internal separation wall between the two piston cylinders, which cannot be fixed short of replacing the valve. The 9100 is not susceptible to those issues, thereby making the 9100 the more durable model which is now commonly recommended for twin tank applications.
It's not starting the regen cycle, and I believe that it's just the settings. I can start a cycle manually.
As an initial starting point, to investigate why tank switch over and regeneration is not occurring automatically, first inspect the entire length of meter cable which is plugged into the top of the paddle wheel flow meter on the outlet connection to the side of the control valve. The cable runs through the rear of the controller, terminating at the drive gear which causes the Capacity wheel on the front of the controller to slowly turn whenever soft water is exiting from the softener. Since your Capacity wheel has 2150 gallons total possible Capacity, you will not observe much if any movement while allowing only a few gallons of soft water to flow from a faucet.
The cable is a mechanical device, so if the cable becomes worn or broken which can often occur over time, then the cable may not transfer the mechanical twisting force supplied by the flow meter, to the control valve gearing. If the cable remains in good condition, suggest then disconnecting the cable from the flow meter by pulling the ferrule straight outward. Twist the cable between two fingers to determine if the Capacity wheel will turn. If so, it is possible the flow meter gearing is simply worn out, which could require either replacing the entire Meter module, or perhaps only the meter cover which is offered separately. Mechanical meter module shown below.