Wiring ethernet cable from AT&T fiber Modem to a specific room
Your basic plan is just fine. The key problem you are having is figuring out which cable is which. The secondary problem you may be having is making sure the jacks are wired correctly. There are tools designed specifically for both of these tasks. Pros get the good stuff. For a once-in-a-while use you can probably make do with the cheaper versions. A couple of specific examples:
Toner
That's &quot;generate a tone and detect it&quot;, not &quot;powder that goes in a laser printer&quot; :-)
While you can buy a tone generator and a tone detector as separate items, normally you buy them together. Here is one I purchased recently, which I like because it is relatively inexpensive (so I don't get too upset if someone borrows it and breaks it) and it has &quot;ends&quot; for Ethernet, coax, phone, etc. so I can use it for any type of wiring job.

Cable Tester
There are plenty of these around. When I started in the network business, similar devices cost a few hundred dollars - and were worth every penny. I currently have a Klein Tools VDV LAN Scout Jr. Tester:

which includes one adapter for the remote end and gives very quick readings of the status of all 8 pins. There are plenty of others - e.g., some on Amazon for &lt; $10, though some cheapies will last a long time, some will list a reasonable amount of time (1/5 the cost, 1/5 the lifetime and if you only need it once in a while that works great) and some hardly work at all. YMMV.