|"I cannot find this battery anywhere for purchase."|
HUH? I had no problems finding one.
Don't use quotes around the part number or the whole string you search with - in this case the A at the end of your part number may merely indicate the supplier that made it for Apple (they didn't make it) or a minor revision, or the A may be ommited in ads for one.
Search using: pram g4 820-1819-A (no quotes)
Your Pram module, used
It says here there are at least three possible part numbers
Apple Part #: 922-7173, 820-1813, 820-1819
that will work in what you have -
Search using: g4 pram 922-7173
e.g. - A new PRAM module
Another part number - 922-6007
"Apple Part #: 922-6007 or 922-7173"
A link there - identify your model. Apparently, you have an aluminum 15" G4 powerbook (there are also titanium G4 powerbooks, and aluminum 17" G4 powerbooks, that have different pram modules)
Search using: pram g4 820-1813
The 820-1813 and 922-6007 pram module looks different from yours, but if it fits, plugs in the same way and is the same voltage, it will work.