I am already familiar with the use of 沒（有） as the negative of 了 in general. For example such as saying 一些衣服沒有乾 or 我沒有找到, 沒五點 etc. This question is just about why it's one or the other.
I have mostly just learned when to use one over the other by trial and error, and there are times both are okay grammatically.
However, I am sure there probably is a proper pattern to which is chosen, and I just never learned it. I was curious what that pattern would be.
沒 is negation
沒有 is negation of 有 (have). Sometimes 沒有 maybe shorten to 沒. It is not advisable, though.
Neither is a negative of 了, which is a modal particle most of the time, but can also mean "already"
他死 is not the same as 他死了, in fact it is incomplete. 他死了 is complete.
說完 is the same as 說完了
In my opinion
"沒" is like adjective or adverb.
"沒有" much like the meaning doesn't or doesn't have.
But in most conversations, you can actually use interchangeably.
Actually, when emphasising ownership (e.g.I don't have a pen), in some formal occasions, or written language, 没有 is the prefer one, but not absolutely. More than 90% scenarios they can be treat as synonyms.
Same, don't overthink about it. the only difference is one has just one character, the other has two. So if you are running out of time, just say 沒.
有 (have) is redundant in both cases:
一些衣服沒有乾 = 一些衣服沒乾, some clothes have not yet dry. The opposite is 一些衣服乾了, some clothes are dry, or some clothes have dried.
沒五點 is incorrect, as well as 沒有五點. It should be 沒到五點 or 沒過五點. But both 還沒五點 and 還沒有五點 are fine.
有 having 没有 not having 了 already 还没 not yet
衣服干了， cloth dry alread。 衣服还没干， cloth not yet dry。
五点了， 5 oclock already。 还没五点， not yet 5。
I would expect much of the pattern would be related to prosody. In this context, prosody would refer to the natural "chunking" or partitioning of Mandarin. That is, Mandarin seems to have a tendency to "chunk" into pairs of syllables.
For example, I would expect the answer to the question "你有没有钱？" to be "我没有钱", "没钱", or "没有" rather than "没有钱", "我没钱", "没". It is not that the latter are necessarily grammatically incorrect, but they are not as typical/don't quite sound right.
This is also related to the "rule" (not a strict rule, it seems) that a single syllable noun takes it's adjective with a 的 if the adjective is bisyllabic and without 的 if the adjective is one syllable. For example, "绿色的球" and "绿球", rather than "绿色球" or "绿的球".
I think this tendency is also related to the reason why so many Mandarin words are two syllables. It also relates to how to break up a series of third ones for tone sandhi; many of the lexical chunks tend to be two syllables (see this answer, for example).
The above "rules" are by no means strict. Also, I am not a native speaker and so welcome any corrections to my examples. I also welcome any suggestions for sources, as I forget where I first saw this bi-syllabic tendency.
