By 1913, the company was producing over 500 fine watches a day and had over 500 employees. I have an Illinois of my grandfather's as well.
By 1917, serial numbers were 3,000,000; 3,200,000 in 1918 (thus easy to date by serial no.).
The Bunn special was their best railway watch.
First watch produced in 1872 at the Springfield, Illinois factory.

Pictures and ser. nos.:
Illinois

The pictures of sale items at this site may show your model, if you don't already know it.
Illinois sales