By the time of the mountain howitzer, the linstock was a backup device as the friction primer had been adopted for US artillery pieces. Friction primers are something of a problem for most hobbyists so we use something else.
You don't say whether you are looking for a period design or just something that works and is easy to construct. There have been threads about the latter; I can't remember any on making a period linstock.
I will check my doc when I get home and see what I can find. Consulting my doc, I find that the late linstock is a very simple piece, basically a 1.5" dowel 33.5" long, with a 3.5" metal cap with a cross hole for the slow match. There is a iron point on the opposite end which is tapered to about 3/4" diameter where it enters the 2 1/4" long point. There are a few more details available from AOP No. 40 Equipment Drawings for Civil War Field Artillery.