I'm creating a character with a Guild Artisan background as a tailor, but I'm not sure what tool would be good to get proficiency in.
Building on LyreCode's suggestion, the weaver's tools would be the best choice for a tailor's artisan's tool. In fact, I have semi-recently (as DM) helped one of my players create a PC who was previously a tailor before they become an adventurer, and we settled on choosing these tools for the reasons below.
There is information on the weaver's tools in XGtE, p. 85. In particular, the opening sentence says:
Weaver's tools allow you to create cloth and tailor it into articles of clothing.
Ok, so the word tailor here is used as verb rather than a noun, but this description still describes a tailor pretty well (certainly more so than any of the descriptions for the other artisan's tools).
Furthermore, that page contains a few sub-headings under Weaver's Tools, including the following:
- that the tools themselves include thread, needles and cloth, as well as the fact that you know how to work a loom;
- that you can inspect and determine attributes about various cloth objects, including tapestries or clothing;
- that you can repair clothing, and that you can create items of clothing.
I'm not going to quote all of that here, but it's all very indicative of what a tailor's profession would likely entail.
Weaver's tools would probably be best.
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