Here in the summer months I always carry a towel. But I'm an old fart that don't follow the rules, just do what works for me. I use a small hip pack to carry my phone, keys, MP3 player and a bit of trail mix. Since I always have that with me (same pack as I switch amongst 8 bikes all year), in the summer I have a neon yellow microfiber towel clipped to the belt, on the left side. Does three things.
a) mops sweat that pours out whenever I stop for a drink. I never stopped before to drink but, of course, this year I have to.
b) waves and flops around in the breeze which improves my visibility. A driver's eye sees motion, wierd motion so it helps.
c) good for drying my hands when I wash them. I don't want to touch anything in rest rooms anymore.
Watch carefully how long it is if you do the same. Must keep it out of the rear wheel.