黙然 has two different readings which are もくねん and もくぜん. I am fairly confident in saying that もくぜん is the more common of the two and that もくねん is some sort of outdated reading. Is this interpretation correct?
黙然 is an uncommon word and I cannot say which is more common from my personal experience, but according to ふりがな文庫, もくねん was much more common roughly 100 years ago. And I see no reason to believe this ratio changed greatly after this period.
Note that ふりがな文庫's data are based on explicit furigana in relatively old novels, so rare, nonstandard or creative readings tend to appear more common (だんまり should be an example of this). Still, I think the figures are meaningful regarding もくぜん vs もくねん.
I’m Japanese and always pronounce this “もくぜん”. But I’ve found “もくねん” is acceptable.
ふりがな文庫 has many words usages in literature. It’s so useful for searching correct and traditional usages for writing. But there are some old usages and few or no usages for speaking. For example, 増長天王 was written in 1927.
So I can say as you expected, もくねん is a bit out of date.