Here is a detail of Plate 151 in Delaporte & Garnier, [i]A Pictorial Journey on the Old Mekong," originally published as part of the Mekong Exploration Commission's report of their journey to the headwaters of the Mekong River in 1866-68 & reprinted by White Lotus (ISBN 974-8496-76-7 or 1-879155-76-1 - not sure why there are two). The caption identifies them as "Annamite" (Vietnamese). The hat on the man to the right is not an exact match, and he is a civilian, but note the little cone on the tip of the hat, similar to yours. Whether it is coiled or slat construction cannot be seen.
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