(I can't measure the current through the clock without
'breaking-open' the circuit (ammeter must be ins series), which I
don't want to do.)

I'm probably missing the point but I'd thought that you would have
access to the terminals to which the battery was connected and so could
connect across them a resistor of (say) 470k [1] and then measure the
voltage and current when the cells are in sunlight.


[1] total guesstimate based on a Lion cell requiring a charging voltage
of ~3.6V and anything less than a few microamps not being worth the
candle

--
Robin
PM may be sent to rbw0{at}hotmail{dot}com