If you are plugged directly into the panel why would you use a timer ? Just makes things more complex for no apparent reason.
And the problem doesn't seem to be the battery so why try to solve that ?
Problem (apparently) is the controller. I have two of these :

Had them about 3 years. Both work fine straight out of the box. They have loads of settings but I just used as plug and play, never fiddled with anything on them.
Right now one is on a 12v panel / normal supercheap auto car battery (not a deep cycle one) / water pump for horses / shed sink.
Other is on 12v panel / electric fence energiser (DakenAg or Speedrite can't recall) / old 12v battery from my tractor which I replaced (but problem turned out not to be the battery and it still works fine on the fence). I have this set-up in an old esky and also use it as a jump start battery for everything that doesn't start, so have extra output terminals connected directly to battery as well as the fence charger coming through the controller. That way I can flatten the battery trying to jump start something if I so choose.
One used to be on 24v battery in another tractor that I also ran lights off in my shed. Hardly every used the tractor so just had panel to controller, controller to tractor battery and controller to shed lights all on Anderson plug so I could disconnect whatever and drive off if I wanted.
I've never had an issue. I never changed any settings when I went from 24v to 12v. And they cost $10 not $30.
You sure you have it wired like above, with the pump where the bulb is and
you don't have anything other than the controller connected to the battery ? So just one +ve wire and one -ve wire from battery to controller ?
(and you also connected the battery to controller BEFORE you connected panel to controller or pump to controller ?)
(and a 24v solar panel for a 24v battery ?)
**edit : can't believe your solution to "cheap Chinese crap" is to replace a simple and robust system using an Australian bought battery with more "cheap Chinese crap". I'll give those capacitors 3 months exposed to farm conditions. Terminals will corrode with cow piss or something.