4/4 gets 1 and 3 as strong. 3/4 gets 1. 6/8 gets 1, and 4 is strong but less so. I don’t know what 7/4 is supposed to be, but 1, 2, and 5 sounds good. 9/8 and 12/8 are really just 3 and 4 triplets, respectively, so they get 1, 4, and 7 and 1 and 7 respectively. I am also aware that beyond some number relative to the denominator (I think it’s 9 for */4), you just subdivide into smaller units. What’s the general way to find where beats should be emphasized for a given time signature?
You're right with the more common ones, and 12/8 works rather like 4/4 with triplets.
Odd ones, like 5/4, usually work in twos and threes. 5/4 in 'Take Five' is 3+2. 7/4 is often 2+2+3, but if the writer wished, could be 2+3+2, or 3+2+2. Get onto something like 13/4 - I used to work with a Greek band - and it was 3+3+3+4.
So, generally speaking it's up to the writer, who may give a clue at the beginning, or beam appropriately - difficult with no quavers - but 3s and 4s (and 2s) are the order of the day.The ony general way is to listen and count. If sight-reading, look out for what could be the more emphasised notes, such as 1s, 3s and 5s of the underlying harmony. Those are often naturally emphasised in 4/4, so why shouldn't the odd ones follow suite?
Much depends on the composer's intent. For example 7/4 may be broken down into 4/4+3/4 (sometimes written 4+3/4) which is fairly easy to read. It could be 3/4+4/4 or 2+2+3/4 or 2+3+2/4 or the like.
In some cases, beaming is helpful. Alternating 6/8 as 3/8+3/8 and 3/4 ("America" from "West Side Story") could be shown by beaming the 6/8 measures as 3/8 by 3/8 and the others as 3/4.
There's no obvious way for things like 55/64 or the like. The composer has to give a hint (or several hints.)
9/8 commonly gets the three pairs and a triplet treatment out here. That piece usually goes with
•·•·•·•·· and then occasionally throws in a
•·•·•··•· for syncopation
Technically, the time signature implies nothing about where the beats go, but there are common patterns that come with specific genres.
PS. Hoping my just-invented beat notation is readable…
As the other answers say, there is no rule that is inherent in the piece itself - the same time signature can be subdivided in different ways.
However, you can get very strong hints from the history of the piece. Before the 20th century, you will typically find uneven metrums in the folk music of countries with Turkish cultural influence. Within these countries, the metrums tend to cluster in different regions. So a folk dance in 9/8 from Southwestern Bulgaria is almost certain to be 2+2+2+3, while a folk dance in 9/8 from Northwestern Bulgaria may well be 2+3+2+2 (note, local performers are unlikely to know the formal name/division of the time signature, but they will readily recognize names for them, usually the name of a popular dance with that time signature).
In a sense, this is no different for the even metrums you mention. There is no unbreakable rule that 1 and 3 are the on-beats in a 4/4 signature, it's just that this is the common way to do it for music written in our own modern Western culture.
The standard numerators are 2, 3, and 4 for simple meters (beats subdivided into two parts) and 6, 9, and 12 for compound meters (primary beats subdivided into three parts). For quadruple meters (four primary beats per bar, i.e., numerator of 4 or 12), the third primary beat has secondary stress in each measure.
For all other numerators, the patterns can vary, as other answers have already detailed. But generally beats tend to be grouped into 2s and 3s.
One thing I'd add to other answers is that it's most typical for a piece to adopt a particular subdivision throughout (like 5/4 may be a 3+2 or a 2+3 and it's consistent), but there are pieces where this is not true. Some music will explicitly indicate this in a time signature (e.g., (3+2)/5), but in many cases you just have to figure it out based on rhythmic patterns or style/genre. I've seen several pieces where bars alternate in a 5 pattern with 3+2 one measure and 2+3 the next. And sometimes the pattern gets altered just for a single bar somewhere, creating a sort of "syncopated" feel. (This happens in other more standard meters too: for example, a piece in 6/8 might just throw in a single bar that feels more like 3/4 sometimes to change up the pattern.)