Some theoretical background:
Be7 beta decay happens by way of electron capture; one of the atom's electrons gets turned into a neutrino.
However, the charged weak interaction has a range of 10^(-17) m [Compton wavelength of a W particle], meaning that it is effectively a contact interaction. Meaning that an electron has to be at the nucleus itself in order to be captured.
This becomes more likely if an atom gets squeezed, which is what accounts for the observed Be7 effect. However, the electrons most affected are those in the highest-most orbit shells, those with the smallest orbital energy and largest extent. This is why the effect is much more difficult to observe with potassium-40; it has more inner electrons than beryllium.
Beryllium has shell structure 2-2
Potassium has shell structure 2-8-8-1
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