Brian - that small button is called the "Lock Assy, Release". For some reason they don't show it in the parts diagram. They actually list it under the components of item 4 in the pic. It's Part No. IH 401449-R1 and appears to still be available. Recommend you contact one of the Sponsors listed in those boxes above to order one.
Now, this little button is a "self contained spring loaded assembly", and it is a "press fit" into that little hole in the lift arm. I don't know how others install it but I usually use a small socket equivalent to the area around the outside of the button (not the actual moving button part) and a pair of pump pliers (channel locks) and a rag around the rubber grip. Using these things I carefully press the button into the arm. Sometimes it slips off and I use a few cuss words, and sometimes it falls back out if not pressed in enough and I use a few more cuss words. The dang thing is hard to see if it's pressed in enough do to the rubber grip. If it's not to costly you might want to order 2 and keep one on the shelf in case it falls out again. Maybe someone else on here has a better installation method and will let us all know.
Don T - those alligator clips are supposed to have little covers over them so your fingers are isolated from the contact (and so you don't burn your fingers). And by the way, did you find them in the Flower Power section of the Garden Dept?