I see the same rapid voltage fluktuations on some of my old batteries. And on new small scooter and motorcycle batteries.
Scooter and motorcycle batteries can be a small as 4Ah to 12Ah.
This is one of the reasons that voltage meters is not the only (or optimal) way to determine how much energy is actually stored in a lead acid battery.
The voltage only shows how well, those parts of the surfaces of the battery plates that still works, are charged.
But if you are down to only 10% of the plate surfaces are still functional, then you are down to only being able to store 10-20Ah of energy is those "old" batteries.
It seems that some lead acid battery designs can only be "deep cycled" 2 to 10 times, before they are worn to the level where they have less than 10-20% of their original capacity left. Even if they show being charged to voltages way higher than 12.6V
I have no idea of how many deep cycles your particular batteries can withstand, but it sounds like they have been "deep cycled" more than 10 times.
For some AGM batteries I have seen claims of three times as durable. But if that is just three times more of 2-10 times, then it is still only 30 deep cycles before they are toast.
So my thinking is, that low cost sealed batteries, may still not have very many times they can endure the deep cycle, even if they claim to be better than......
So the advice to never take a lead acid battery below something like 12V (or even 12.2V) is probably good advise for most lead acid battery designs. And in particular for sealed designs.
