On my #1902, the gray cap is on the side opposite the flag.

I wouldn't consider this a variation, but a painting 'style difference' In the early years, color control wasn't as precise as today and the differences in color intensity, the 'blooms' on shrubery, etc. could vary quite a bit from one painter to another. Others' may feel differently, but in general, a recognized 'color variation' is one which the company ordered during a production run. This would include: green-to-blue water on New London Ledge, Minot's, Barnegat, and Michigan City, Brick color change on Round Island, Tan-to-grey tower on Beavertail.