I've been working with a thin 3M 7847 laser marking tape, and tried various ways to hold it still while I was engraving it.
What I finally settled on was a simple jig that I made using two very thick 18" straight edges and a piece of thick acrylic.
I use a very light temporary repositionable spray adhesive on the acrylic to hold the tape in place.
I also made a simple template which I engraved onto the jig itself. This means that I can push the jig flush against the edge of the engraver to get consistent positioning of the origin each time.
I made it at Techshop!
Step 1: Material acquisition
I also used a piece of green acrylic, 24"x10", that I bought at Techshop. I used ~1/4" thick acrylic so that it would be rigid.