I have two bedside swag lamps, one on each side of the bed. Each one has a plug that goes into the wall. They each have a pull chain for use in turning them on. I would like it if, when I pull the chain on one lamp, they both would turn on. Is this even possible and if so how would I accomplish it? I am hoping there is some special plug I can buy, plug both lamps into it and be done...
I've never seen a wired set up where when one light turned it, it also turns on another device. You can, however, go with wireless devices. They range from basic RF (radio frequency) devices to z-wave and WiFi devices.
If you go with a smart device, you can add other lights, locks, speakers, etc., over time. Google Home, Samsung Smart Things and Amazon Alexa are examples of smart device hubs. You need a hub if you go this route and make sure the devices you buy work with the hub.
Here is a simple RF device just as a example (not a smart device). You'll need to research it and other like items to see what would work best. https://www.amazon.com/dp/B01HWB0TPU/ref=cm_sw_r_cp_apa_C.MYBbT3DPGYV