Hopefully your gremlins will sound familiar to some other unlucky soul and you will get your answer.
I can offer a weak test: some folks who have had weak batteries have used the manual decompression lever to take some of the heat off the starter just for a wee bit o' time - don't hang on the bugger! But I tend to agree that 12+V should do something better than "clicking".
You don't have access to another similar battery that you know is good? Hopefully someone will post how to test the regulatory rectifier for ya.
An "electrical" link from the index:
(check out Happe's regulator tests