An ongoing debate: two 12V lead acid batteries connected in parallel - some propose some sort of see-saw current self discharge of the pair; I see no theoretic or empiric reason this should or does occur.

I agree with you... theoretically two 12Vdc batteries connected in parallel will cause the voltage levels to equalize in each. Assume both are of equal size and in good condition with one charged (2) volts higher than the other... (ignoring any impedance losses) I would expect one battery to end up with a (1) volt loss and the other with a (1) volt gain...
At that point any transfer of charge would cease...
If you draw this as a simple diagram with two equal batteries connected positive to positive and negative to negative... or in parallel, since there is no difference of potential across the connections there will be no current flow.

By the way, this is done frequently with UPS, Solar and other storage setups...

I would like to amend my comment to add that in actual practice, given environmental conditions, temperature, etc. there is likely some leakage that may cause a "see-saw" condition... but all things being equal any discharge would likely be small and very slow...
Was this purely a theoretical discussion?

Thanks,
Not coming from a theoretic basis - someone asked on a discussion board r.e. a parallel battery set up for more cranking power for a large block Moto Guzzi motorcycle. One individual with some background in boating proffered that boats are set up w diodes to prevent this discharge. I suspect the diode setup may be to prevent the disaster that would occur should one battery short out and act as a bus of low resistance for the other.
Thanks again