Yes, a 4 port unmanaged gigabit switch will work for that but do make sure the port on that wall is active/connected first.
So my modem/router would be connected to the ethernet port in my living room (I could just connect the streaming box directly to the router since it's in the same room), then for my PC I would connect it to the gigabit switch and connect that switch to the ethernet port in my room, and this will result in the switch and the modem being directly connected even though they're in different rooms?
Consider activating both Ethernet ports so that they connected to your router. Then your PC and TV can use them both for communicating with each other and with the Internet.
To accomplish this, you need to find where the in-wall Ethernet cables converge. There will usually be an enclosure. If you are lucky, the cables will be terminated either with RJ-45 plugs or punched down to female RJ-45 jacks. Either way, you want to connect them to your router. You can also connect them to an Ethernet switch, then connect the switch to your router.
If the router is located elsewhere, but is near an Ethernet wall jack, then you can put the Ethernet switch in the enclosure and connect it to all of the cables feeding the wall jacks. You would connect the router to its wall jacks. This will activate all of the other wall jacks.
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