The wire gauge necessary depends on current, voltage, and operating temperature. I could go into much more detail, but like other have said, 26AWG to 28AWG is plenty for battery to soundboard/buckpuck to blade LED applications at common voltages (3.0v-7.4v). Now if you are getting fancy with surface mount accent LEDs located away from the board, 32AWG to even 36AWG should be fine as they draw so little current.
Sources: As Sevinzol said, CAT5, CAT5e, and CAT6 ethernet cables can be a good source, but I would only recommend them if you already have some on hand, gathering dust. They are expensive at most box stores for the amount of wire you get. an additional concern is that ethernet cable comes in solid core or twisted strands depending for the intended use. Installation cable for putting behind walls is almost always solid core, whereas patch cables are usually twisted strand.
A great source for quality small gauge wire is you local model railroad hobby shop. I picked up some 34AWG paired that looked like tiny speaker wires years ago for a small scale model's collision lights using SMD LEDs and they worked wonderfully.
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