I started researching them and found that linen is the most common fabric used so I picked up a brown striped mid weight linen. I like the reduced pattern in Fitting and Proper by Sharon Burston. This pattern was made from an extant example. I enlarged the pattern and it clearly wasn't going to fit without major alterations which I just didn't have time for so I pulled out the JP Ryan pattern that I happened to have. The JPR pattern instructions have you making the garment by machine. I knew this pattern would fit so I cut it out all in one piece and I used the instructions in Fitting and Proper for constructing it by hand.
Inside of back
The neck edge, front edge, hem and sleeves were hemmed with a 1/4 inch hem. I used a facing at the back neck where the pleats are as turning it in twice there would be too bulky. This is the way the extant in the book was constructed as well.
That was it! No lining or anything fiddly involved with this one. I've already decided to do one with long sleeves: wool lined with linen. It was an enjoyable project.
Here's one view of the short gown being worn: