Here’s my feeder. Each barrel has its own motor, own battery, and own solar panel. I have them set to throw 1 second of corn each, morning and evening. In the event 1 goes down, the other is still throwing. That happened this weekend, barrel on the left has a dead battery which was just replaced this past September, and it’s an expensive AGM battery.

So here’s my thought, running a wire + & - from one battery to the other, to create a stinger 12v, not a 24v. The idea is that if one solar panel fails, the other can keep both batteries charged, or if one battery fails, the other can still power the motor & timer.

Would this work?

If connected that way (batteries directly connected in parallel) and one battery failed, it would become a constant parasitic drain on the remaining good battery and likely drain it dead in short order ( along with the extra load of the 2nd motor).

If your AGM drained due to a failed solar panel, best way to prevent that is to have 2 independent solar panels for each battery.
The solar panels already have an isolating diode in them to prevent back-drain - so one failing panel wouldn’t affect the other one from continuing to charge. 2 panels will also give better charging capacity during cloudy periods.

Also , it is possible, using some large diodes(4), to re-wire feeders/batteries to possibly make it work like you want, keeping batteries isolated - but will 1 good battery & panel even be able to keep up with the load from 2 feeders? Even during a cloudy week? Upgrading to a larger batteries & larger panels both, that could reliably power two feeders, would be much more expensive than just getting a 2nd small panel for each.
The diodes will also cause a small voltage drop(.5 to 1 volt) in operation, and need to be sized according to motor draw.