Well, might as well pop in my dos centavos worth as well.
I happen to be the proud owner of an original IH Pitman Arm. It still has the part number on it and is still painted Cream!
That one ain't gonna get used at all!
I also agree with Russ. From a wood standpoint the ash, especially white ash is a great wood to use in this application because of its flexibility. It is also a slightly wider and looser grain than oak - hence it's ability to flex - actually more like whiplash under stress. Making a pitman arm from wood is very easy, probably would take about an hour to make 3 or 4, which is what I would do. Best to have a couple of spares hanging around.
The hardest job (read time consuming) is to lay it out. Basically all you need is access to a drill press and a bandsaw. lacking either one, then a back saw and a portable drill will suffice if you take your time.
If you do not have access to ash, then I probably would choose white oak. Birch and maple I would hesitate with as they can be brittle and snap easily. Another good choice would be southern yellow pine - high oil content and resists rot and because it grows quite straight, the grain is true and highly resilient.
As Russ also said, 2 or 3 coats of tung oil is a good choice, however, they used to be coated with just boiled linseed oil in the past and when nothing else was available - good old 5 or 10 weight oil
Also, I would re-coat the pitman arm with oil in the spring before you start mowing and again in the fall when you put it away. It takes 5 minutes, but is well worth doing.
I do my horse hoe and my log wagon eash spring and fall. They will last for years as the water beads off and does not get sopped up.