Unangbangkay

sadly wa and ga aren't that clear cut, but I think I know where you are coming from re definite and indefinite nouns in the sense that ga is used for new information and wa is used for old information (see no. 2 below)

so many functions are packed into each of these particles so there's no single or simple rule for using one or the other, and they also have a lot of overlap between them (they both can mark the subject of a sentence/verb phrase - this is the way they behave similarly in sentences, as you say) which is what makes them so difficult to get a grasp of for people learning JA as a second language. I only dabbled a little bit in JA language education studies but based on that and from what I've read and experienced, I can list three "rules of thumb" that may help:

• wa has a larger grammatical scope than ga
• ga has a tendency to be used for new information and wa has a tendency to be used for old information
• wa implies an exclusion of other possible things and ga is more neutral in that respect

let me go into a little more detail

1. wa has a larger grammatical scope than ga

let's take the typical example of ゾウははなが長い (zo wa hana ga nagai - "elephants have long trunks", or "the elephant has a long trunk" which would fit your heuristic exactly). The elephant is the main noun in the sentence - the trunk (nose) belongs to the elephant, and the feature of having a long trunk is a characteristic of the elephant. in this sense, the elephant "owns" the entire sentence, and this is what i mean by "grammatical scope" (it might not be an accurate use of the term but I'm using it a bit liberally here). the elephant is marked with a wa because it is the main subject in the sentence (and all the other parts of the sentence relate to it), and the trunk is marked with a ga because it is the secondary subject in the sentence

2. ga has a tendency to be used for new information and wa has a tendency to be used for old information

let's take an example from the start of an old tale called momotaro: むかしむかし、あるところに、おじいさんと、おばあさんがいました (mukashi mukashi aru tokoro ni ojiisan to obaasan ga imashita - "once upon a time, in a land far far away, there lived an old man and an old woman"). the old couple are introduced at the start of the story using ga. In the very next sentence they are marked with wa: まいにち、おじいさんは山へしばかりに、おばあさんは川へ洗濯に行きました (mainichi ojiisan wa yama e shibakari ni, obaasan wa kawa e sentaku ni ikimashita - "every day, the old man went to the mountainside to cut the grass, and the old woman went to the river to wash clothes").

3. wa implies an exclusion of other possible things and ga is more neutral in that respect

let's take an example of a conversation about doing one's homework
A: 宿題をやったか？
B: 宿題はやった。
A: ほう、じゃあ何をやらなかったのかな？

A: did you do your homework?
B: I did do my homework
A: uh-huh, so what didn't you do?

the wa here implies that there is something that B did not do but could have been expected to do. the neutral particle in this case would be を because the homework is the object in the sentence here. you could have a similar example in the response to a question like "who went to the party yesterday?" - "X wa itta" would imply that person X did go, but person Y (and perhaps person Z etc.) who would have been expected to go (especially if X was going) did not go. otoh "X ga itta" would only mean that X went and doesn't necessarily imply whether other people went or not

tofugu has a text post with many examples and some additional rules of thumb as well as a video post on this subject. I haven't checked the whole thing but the text post looks pretty solid at first glance. (Another thing that's also given in the tofugu text post is that sometimes it's simply better to omit the noun completely if it can be inferred from context)

the best way to learn is to practice and get feedback on usage of wa and ga - i can help with that on discord or elsewhere if you like. also send a follow-up q if you didn't get any of the above or any of the details in the tofugu stuff (there is a exclusionary feature of ga that seemingly clashes with what i said in no. 3 about wa above but both of them apply and i can't really explain it well at the moment)