till not sure what type of gate you are looking for, went thru my Japan pictures, didn't really have any good pictures of garden gates. Lots of temple and castle gates, but not garden. This is what I found, large images to show more construction detail.
This is what I imagine you are looking for:
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its really a picture of the house, the car kinda blocks the gate. I've stayed in the house several times, so have looked at the gate in detail. The joinery is nothing special, through tenons for the beams, the roof boards are nailed on.
I have many temple gate pictures, this is from Ginkakuji in Kyoto:
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a whole lot of detail visible, it was originally the garden of a Shogun's palace, so this is sort of a garden gate. Doubt you want to build anything quite this big tho.
As for garden walls, this shows the construction of a wall in Kumamoto Castle, upper class garden walls are built the same way:
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the typical through tenon, wedged on the top.
As for joinery details, not free, but I have and like this book:
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Brian Huffaker, DSWL