Gyro and Siwastaja, Thank you.
From the looks of it and comparing to the China e-bike super cap/battery, it would seem to be one such; I will search more thoroughly to glean any more available info.
I had to keep the terminals shorted directly- no ammeter- by a 14awg×<50mm long copper wire for over an hour to bring down the (shorted) voltage from 7mV to under 1. Removing the short, I find that the (open) voltage rises once again gradually, and has reached >500mV in just 3min., and still climbing. I suspect the internal connection to the much distributed electrodes constitutes enough (internal) resistance to prevent evacuating the whole of the charge by external terminals alone. And then every electrolytic capacitor behaves similarly, more or less.
I am quite convinced that it is a super cap and not a voltaic battery, though the similarities in construction retain vestiges of voltaic action in what is really a super cap, especially near voltage zero.
The China e-bike "lithium" super cap battery seems to be always 3.6V, and if this applies, perhaps there are no series connected cells after all. 3.6V may also be exaggeration, more like 3.0. Still, I continue to be bugged to find a way of setting a decent rated voltage for it.
Edit: I hate it when an OP drops his subject without a logical end. Not me, and so:
Picking up from Siwastaja's sugestion, I tried to discharge the "super cap" well as could, but even an hour of bolted short would not reduce the subsequent open circuit voltage to zero. It picked up again to 0.65V in half an hour. My inference of voltaic action in super cap may have been, to say the most charitable, far fetched. And so, I tried recharging from 0.65V with a controlled 1.0A input, hopefully to reach 1.65V in a long time. Lo and behold! It took less than 5 MINUTES to reach 2.6V! And so I learnt to treat it as a Lipo, and continued charging at the same 1A. 6.5 hours later, it reached 3.5V; charging was enhanced to 2.0A and another two hours on, it is still 3.55V.
The cells of all the other batteries I picked along with this are LiFePO4, and so may be this unit. I am limiting charge to 3.65V just in case: I expect over 20Ah to go in!
Needless to say, the charging battery is kept outdoors and well clear of inflammable stuff. So far, it has stayed cool to touch.