This is shielded cable and that will cause problems tracing it.
Are the far ends terminated? If yes, the I would suggest what you need is a cable mapper with multiple remote ends like the Platinum Tools T129 VDV MapMaster and optional T121C Twisted Pair/Data Remote Set, 19 pc.
https://www.specialized.net/Special...ter-20-Voice-Data-Video-Length-8940.aspxThis is just and example.
The fact the the cables are in bundles of 24 tells me that each bundle goes to a specific area and once you find a couple of bundles far end you should be able to see a pattern emerge. I would also add that this is a two person job in my opinion
Not trying to bad a hardass, but I see you're from California. Due you have a proper Contractors license for doing this job?