Another detail we can add is that we know there were also special band looms that made brightly colored edgings or braiding. Such edgings are hinted at on some Hittite vases. Here are some musicians and dancers on a vase in the Corum Museum. The lines on their skirts may also indicate pleating.
Such fancy trims and pleating are much more visible on the Minoan and Mycenaean frescoes, but it’s best to remember these ladies are from a somewhat different period and place than my Trojans and Hittites. They do provide the only color vision, so it’s worth comparing. Here is a Minoan fresco from Akrotiri, island of Thera, with a beautifully dressed lady of the court: