Mudski... the Reg is designed to switch automatically between 12 and 24 volt solar panels not Batteries. The battery has little to do with it once the panels are connected.
As mentioned prev the load light is "On" because the battery is capable of supplying the load.
Pls excuse the boldface in teh next bit, I did it to highlight what I think is happening from your description and not meaning to be at all insulting...
The "charge" light will illuminate only if there is sufficient solar input to run the load (if connected) AND something left over to charge the Battery OR there is no load just a 24 Volt battery bank and the panels are 'charging' itBUT the battery bank voltage MUST be over 19 odd Volts IF there are 24 Volt solar panels connected. Any battery voltage under 19 volts is considered a fault and the lo voltage cutout activates to prevent damage to equipment.
As Cupp said... a 24 volt solar system won't charge a 12 volt battery with that Reg you have.
A point to note here for everyone (and I see it occasionally) is that if you deplete your battery during the night or very cloudy weather below the Low Voltage Cutout setting of your Solar Reg you will need to temporarily jump another battery or partially charge the flat one with a Charger to fool the Solar into coming back on.
It happens often enough out bush that I get gifted the odd couple of cans every now and then getting peoples systems going again.
Disclaimer... it can be a tad difficult trying to fault find on the 'Net and there could indeed be faulty gear involved. The above is just my wild hairy rrsed best guess