I don't know what it is called today, but I have had for years a tool called a bodkin. It is metal with a small ball on one end and an eyelet on the other end. The ball end is used to turn corners, and the other end helps guide elastic or ribbon thru a casing. In my day every self-respecting seamstress had one. I think they still make them. They are inexpensive and should be at a good notions store.
Happy quilting
Severna