Here is my ideas - I am a RABID crafter!! Back in the 1970's when I was a girl they used to make a Thinline Paint pen brand called "Liquid embroidery". Now I would NOT suggest THIS product because it stays wet for a couple of hours and your autographs would smear, BUT they sold an embroidery hoop that had a solid base for use with it - instead of the big hole hoop. I recommend looking for one of those.
If you can't find that and really, you probably won't - try this. At your local crafts store buy Sharpies or Permanent Fabric pens in colors that will show up well, Check to see that they are quick to dry. Also buy a smallish 3-4 inch embroidery hoop - The cheap wooden ones are great. When you get home - take a clean and washed, discarded butter or cool-whip lid and trace the outside of the inner hoop - the one without the fasteners. Cut this out and duct tape, or hot glue it over the inner hoop. place 1 layer of your pillow case over the now solid hoop and clamp it down. Your character can sign inside the hoop. Next character - just loosen and scoot the hoop over - so they can sign in an empty space - and you can guide where they sign.
When you are riding just fold the whole thing up and keep it in it's own ziplock baggie clean and dry. Secure the caps on yopur pens each time you put it away though. Accidental smudges will ruin your efforts.
This is such a cool idea, This will bring back good memories for a lot of years- I would LOVE to see pix when you get back!!! - Hugs from Pixie VaVoom