First, eBay requires all images to have a minimum size of 500 pixels in one dimension. You can submit an image of 500x300, but you cannot submit an image of 490x490.
Second, I have always understood (and found) that the maximum resolution is 1600 pixels in one dimension, and if you submit an image that is greater than this then eBay will reduce it to 1600 - I've noticed this in the past, and I've found their reduction algorithm is poor and degrades the image, so I don't submit anything above 1600 pixels in one dimension.
Third, I've also understood that 1600 doesn't work well for mobile users, which make up the majority of people viewing listings. I have no idea where I got the following, but I once researched the best balance between detail and mobile-friendliness, and found the recommendation to be 1200x1200.
So, we use 1200x1200 for most images, and most images are square. But if an image is rectangular, then we will keep the shortest dimension no more than 1200, and the longest dimension no more than 1600 ... for example we might submit 1100x1600 or 800x1600 or 1200x1500 ... but not 1300x1600.
