Trouble With R45 Connectors

Use a "soft clamp" to hold the two ends next to each other:-

Then use a multimeter to check for continuity between the visible contacts:-

1 - 1

2 - 2

3 - 3

6 - 6

Most ethernet links only use pairs 1 and 2

568B is more common (here) than 568A

You may need to "tie" sewing needles to the ends of the probes with copper wire to get access to the contacts. I have tiny "pogo nails" from in circuit test fixtures permanently fitted to my multimeter probes.

<...need to "tie" sewing needles to the ends of the probes...tiny "pogo nails"...>

Small paper clips can also be an asset here.

On your list of problems you forgot low quality or counterfeit cat5 cable.

I once accidently purchased what looked good but turned out to be copper plated steel wire. I was perplexed for a while because the continuity from my cat5 rj45 tester showed it was good. I made a 3 foot patch cable and it worked but a 10 foot one didn't.

I use a Southwire cable tester. You have (2) pieces one connect on each end, It’ll tell you which wire you have a problem with.

https://www.southwire.com/tools-equipment/vdv-tools-testers/m550-continuity-tester-for-data-coax-cables/p/p-58745040