たい
tai
たい is a hand reaching out of you
The picture A hand stretching forward out of your own chest. That hand only ever grows out of you. たい is the hand growing out of you; たがる is watching that same hand grow out of somebody else.
Where the picture shows up in たい
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the hand reaching now
今日は早く帰りたいです。
kyō wa hayaku kaeritai desu
I want to go home early today.
A hand stretching from your office chair all the way toward your own front door.
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what the hand grabs
冷たい水が飲みたい。
tsumetai mizu ga nomitai
I want a drink of cold water.
Your hand reaching forward and closing around a glass of cold water.
Before たい, が sounds more natural than を: the noun is what pulls you, not what you act on.
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a hand held out gently
ちょっと相談したいんですが。
chotto sōdan shitai n desu ga
There's something I'd like to ask you about.
A hand held out only halfway, stopping there to read the other person's face.
To a superior, したいんですが lands softer than したいです.
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a hand you reached long ago
昔は看護師になりたかったです。
mukashi wa kangoshi ni naritakatta desu
I wanted to be a nurse back then.
In an old photo the younger you reaches toward a nurse's uniform; today that hand rests at your side.
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pulling the hand back
今日はあまり残業したくないです。
kyō wa amari zangyō shitakunai desu
I'd rather not work overtime today.
The hand you were extending pulled back in and tucked into your pocket.
All of it in one picture
たい is one hand, not five rules. Reach it now and it is today's wish; close it around something and が, not を, stands in front of it; hold it out halfway and it becomes a careful request. The hand you reached long ago stays as たかった, and the hand you draw back becomes たくない. So the one thing to memorize is not five uses but this: the hand only ever grows out of your own body.