So we know the drive is OK as you can prep it up externally on a second Mac. So that points us to something within your system that needs looking at. OK here's my list of things to do:
Check your systems firmware to make sure its the newest. Follow this Apple T/N: [https://support.apple.com/en-us/HT201518|About EFI and SMC firmware updates for Intel-based Mac computers]. You'll need to us an external boot drive (USB thumb drive or your external case with your new drive in it) to copy off from the other system the firmware updater and then run it on your system. If its the equal or you have something newer then what the T/N has then you're OK.
Then that leaves the drive cable. You'll need to replace the HD SATA cable. Here's the IFIXIT guide: [guide|10379|MacBook Pro 13" Unibody Mid 2012 Hard Drive Cable Replacement]. These cables have a bad track record of failing. In your case it sounds like its just on the edge. Carefully place some electrical tape where the cable bends over a sharp edge and make sure the rubber shock grommets are present on all four of the drives mount points.