A neighbor, somehow, knows, when I connect to the Internet - and begins shooting something at my home (ice pellets). Is there a way to prevent people from seeing my SSID/internet connection? We are on cable Internet; I heard that was akin to a party line.
Since you are talking about SSID, I assume you connect over a WiFi Network to your cable modem.
WiFi is open in the sense that anyone can listen to the packets anyone exchanges with the WiFi access point, even when the connection is encrypted.
It only requires a WiFi network card/USB Stick etc. working in promiscuous mode, and you can see all packets in the air, of any network. With this, it's possible not only to see whether a device connects to any network, but which device, for how long, and how much data it exchanges.
This has been done for various purposes, one is to keep track of employee's work hours.
Here's more information about the topic, but a quick google will reveal much more: https://www.howtogeek.com/196998/your-devices-broadcast-unique-numbers-and-theyre-being-used-to-track-you/
The only reasonable way I can think of to perform this idea, would be that your neighbor somehow has access to your network or one of your devices, while he's inside your network he's able to know how many devices are turned on because they have an IP.
In another scenario we can assume also he has access to one of your devices remotely, in this case a computer for example, which once it's online it will be available to be monitored remotely by your neighbor in the imaginary scenario where he compromised your computer.
At last in the worst scenario, he's constantly watching you through your windows or possibly with remote wifi cameras he installed in the possible scenario where you invited him to your house, went for a leak and he quickly installed a remote wifi camera running to see yours wifi's password and installing into a secret place where it's available to see if you're sitting by your computer, therefor he'll be able to see if you're using the internet.
Also he could've access to your router, on this other scenario we can assume that you didn't setup any new ceredentials for your router and it had default password, which is a known vulnerability in a lot of ISPs.
Well Think about it, try to talk to your neighbor he might be doing something illegal, or he's just a rebel human that wishes you to feel his attention using ice pellets against your house which could be the best scenario hopefully really