Another Tompkins Drum Pops Up on the Internet
The military tenor drum in the exhibit was made by William Tompkins & Sons, MFG., New York. It was used by George H. Cook in 1861. Cook was chief musician of the 27th Regiment of New York State foot volunteers. He lived in Riley Township, Clinton City, Michigan, for seven years after the war.
Website of the Michigan Historical Museum.
The painting is reminiscent of a seated Lady Liberty and a New York theme (Excelsior) which would make sense since Tompkins worked from Yonkers, New York, but I have not been able to find any depictions aside from those on coins.