The answer from @hippietrail's correspondent is pretty much on point, but the specifics have not quite been dealt with fully. So:
Sabbat-ismos "sabbathism, sabbathisation, sabbathising" is indeed a deverbal noun, arising from the verb sabbatizo "to act in a way associated with the/a Sabbath", i.e. "to observe the Sabbath".
Some specific questions: Does it self contain any indication of an article (definite or indefinite)? in other words, of itself would it be "a keeping of the Sabbath" or "the keeping of the Sabbath" or do words using an -ismos ending depend on the surrounding text for any article?
Ancient Greek nouns could be definite or indefinite in the absence of an explicit definite article: the definite article develops only gradually in ancient Greek, and even in Koine there are contexts where Greek does not use a definite article and English would. But without a definite article, the default assumption would be indefinite.
Would it be the equivalent of a deverbal noun or gerund in English? Would it be "keeping the Sabbath"
Yes. The "ideology" meaning is already around in ancient Greek (because the underlying verb suffix means "act in a matter associated with", and can mean "be a partisan of"). But the point of the noun suffix is to make the verb into an action noun.
Does it maintain any number/gender from its root-- "(I keep the Sabbath)ing"
No, no more than the gerund does in English.