[hvalentim]

Some progress:

1 - Adding a 100 uF electrolytic capacitor to the input line is enough to insure a steady output.

2 - Seems the freak 2v oscillation had some relation with the fact the battery used was an end of life sulfated unit. With a different battery in better shape the oscillation was reduced to half (around 1v).

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it looks like the controller is always commuting from charging to non-charging and the other way around (...)

Precisely. This is what I was reading in the display as well.
Charging - Non Charging - Charging - Non Charging
13,6 -15,6 - 13,6 - 15,6

those 15,6 looks like a bit higher than it should

Yes. It's way too high. But sulfated batteries do have weird behaviors. The battery response might have been confusing the regulator.

Anyway with a different battery things seem to have improved.