There's a lot of confusion about Japanese grammar, that is often caused by trying to understand the Japanese grammar through the lens of the English translation. English and Japanese are structurally very different, so it's not at all surprising that this approach would muddle things.
As an example, you start out by saying, “I know たい means "want to."”
Analyzed differently, all ～たい forms are adjectives that have no objects (since adjectives can't have objects), and these adjectives describe subjects as "desirable" for having the action of the verb performed upon them.
You also say, “I'm not sure what is the subject in the second sentence. If I use "I", then it would be awkward because it would mean "I am want-to-eatable"?”
When using は (in simpler sentences like these), you're not marking either subject or object -- you're marking the topic, the outermost context about which the rest of the sentence describes the circumstances.
Let's look at your sample sentences.
Sentence 1: 僕【ぼく】は魚【さかな】が食【た】べたい。
As you note, a direct translation could be, “As for me, fish is want-to-eatable.” We could render this slightly differently, as “[[As for]{は}] [[me]{僕}], [[fish]{魚}] is [[desirable for]{～たい}] [[eating]{食べ～}].”
An analysis:
- 僕【ぼく】は
The 僕【ぼく】 is marked as the topic with は, so we know that the 僕【ぼく】 is the outermost context, about which we are then talking about other things in relation to that outermost context. English doesn't have this distinction in the same way, so we make do by using the slightly-awkward phrasing, "as for ~,".
- 魚【さかな】が
The 魚【さかな】 is marked as the subject with が, so we know that the 魚【さかな】 is the inner context, about which the following verbs or adjectives would apply.
- 食【た】べたい
While this is translated as a verb phrase, "want to eat", using the two verbs "want" and "eat", this 食【た】べたい is technically an adjective that describes some quality of a thing. In this sentence, it's describing the subject 魚【さかな】 as having the quality of "desirable for eating".
Sentence 2: 僕【ぼく】は食【た】べたい。
As you note, a direct translation could be, “As for me, [SUBJECT] is want-to-eatable.” Tweaked as above, we might have, “[[As for]{は}] [[me]{僕}], [SUBJECT] is [[desirable for]{～たい}] [[eating]{食べ～}].”
An analysis:
- 僕【ぼく】は
The 僕【ぼく】 is marked as the topic with は, so we know that the 僕【ぼく】 is the outermost context, about which we are then talking about other things in relation to that outermost context. English doesn't have this distinction in the same way, so we make do by using the slightly-awkward phrasing, "as for ~,".
- 食【た】べたい
While this is translated as a verb phrase, "want to eat", using the two verbs "want" and "eat", this 食【た】べたい is technically an adjective that describes some quality of a thing. In this sentence, ...
We don't have a subject!
Oh no!
... except, Japanese is a language that allows for lots of omission. Consider these simple transitive sentences:
- 僕【ぼく】は魚【さかな】を食【た】べる。
- → We've got a topic, and an object. Considering the context of that topic, we also know that the subject -- the agent of the verb, the person or thing doing the action -- is the same as the topic.
- 魚【さかな】を食【た】べる。
- → We don't have a subject!
- 僕【ぼく】は食【た】べる。
- → Hey, wait a minute -- we don't have an object!
- すぐ食【た】べる。
- → Ack! Now we don't have either a subject or an object!
Despite the challenges of not having various pieces of information, Japanese grammatically allows all of the above, and listeners (or readers) of the above will still understand what is being talked about.
Getting back to your sample sentence #2:
Unless this is a very strange context about monsters, cannibals, or the like 😄, we can be reasonably sure that the 僕【ぼく】 is not the subject of the adjective 食【た】べたい -- this is not saying that the “[I]{僕}” is “[[desirable for]{～たい}] [[eating]{食べ～}].”
Instead, what we have here is an e̲x̲plicit topic, marked with は, and an i̲m̲plicit subject, which is simply omitted. This is a parallel kind of construction as 僕【ぼく】は食【た】べる, where we don't explicitly mention what is being eaten. In 僕【ぼく】は食【た】べたい, we don't explicitly mention what is desirable for eating. We know that something is desirable for eating, but we don't have the specifics for what it is -- this is saying that, “[[As for]{は}] [[me]{僕}], [something unspecified] is [[desirable for]{～たい}] [[eating]{食べ～}].”
By extension, we know that the desire to eat is what we're talking about, with regard to the circumstances of the outermost context, 僕【ぼく】.
So in translation, we wind up with something that is grammatically quite different from the source Japanese, simply because English is grammatically quite different. Instead of saying, “[[As for]{は}] [[me]{僕}], [something unspecified] is [[desirable for]{～たい}] [[eating]{食べ～}]”, we say “[[I]{僕}] [[want to]{～たい}] [[eat]{食べ～}].”
Please comment if the above does not address your question, or if you find it confusing, and I can update the post accordingly.
