I like to keep an eye on knitting and crochet trends on Pinterest, and I recently came across links to several tutorials for making a snug cowl using a garter stitch rectangle. Unfortunately, all the links I followed were not in English, but the concept is pretty easy.
In the picture above, you see the seam on the back of the cowl. Like I said above, the short side is 3/4 the length of the long side. When you finish the rectangle, you match up diagonal opposite corners, and then make them overlap by 1/4 the length of the long side. Since the long side of this cowl was 16 inches, the overlap for the seam was 4 inches. If the rectangle had been 16x20, then the overlap would have been 5 inches. I finished the sample by working around the openings in lite crab stitch.
Here's a model using a piece of printer paper. Imagine the paper is the fabric you made for your cowl. As you can see, I folded the paper into quarters. You might need to click on the photos to see the marks I made on the paper. In the first photo, the upper left and lower right quarters of the long sides are labeled A and B. You fold the corners so that A and B meet up, and sew them together. That seam is the back of the neck
Once you sew the rectangle into a cowl, fold it in half over itself. You wind up with a sort-of turtleneck collar that has two points in front and is skinny in the back, as you can see in the photo at the top of the post. Having it narrow in the back is similar to the concept of a seaman's scarf, which is ribbed at the back of the neck (and therefore narrow) to help it fit neatly under a coat collar. The examples in tutorials for this cowl I found were all knitted in garter stitch, however there's no reason not to use other pattern stitches or to make it in crochet. What is important is that your pattern stitch be at least somewhat elastic, especially diagonally, and not too thick, as it will be worn in a double layer. The stitch you use should also be reversable, since both sides will be visible while you wear it.
The sample I made used Red Heart that I had leftover from another project, and I made it in open crazy stitch, with a size I hook. Working corner-to-corner allowed me to get my intended measurements without worrying about gauge. Even though the stitch was very open, both due to the pattern and due to the large gauge, the crocheted sample I made was very warm.