I'm basing what I said on the comment I was replying to which said that they _already_ figured out that they have neighbors. Given the level of scientific understanding in the 1600s, it seems highly likely that they'd have to have pretty definitive visual proof in order to know they have neighbors, which implies they can see at least some of what's going on over on the other planet. While you're right that they probably wouldn't be able to see someONE waving semaphore flags or lighting A bonfire, there must be a way to have multiple someones doing such in sync so that it'd be visible. Or more likely, a system of simple machines arranged in an array, with the ability to show either a white or black stretch of fabric. It probably wouldn't need to cover the entire area between machines.
I'll admit, it'd take a lot of effort/money to communicate and it'd be pretty slow, but it's not impossible to happen just decades (or perhaps even within a decade) of when its figured out that they had neighbors. Not hundreds of years.