How can I recover data from a clicking/dying external drive?

Solution 1:

In case the drive holds important data that need to be rescued:

Stop using the drive

Any drive access will further worsen the hardware defects and thus decrease the likelihood of being able to recover data. If the data are vital we should let professionals do the job.

Having said this, we can try to rescue the drive content from an image copy of the data that in the best case we have obtained with a last read access e.g. with ddrescue. This should not be done from a virtual machine (boot a live system instead). See also the following questions and answers here:

How to recover data from a failing hard drive?
External hard drive failing, is backup recovery possible?
Recover files from NTFS drive with bad sectors

Solution 2:

I can feel movement within the drive (it is a repetitive movement that continues for as long as the drive is plugged into the laptop via USB).

The repetitive movement you can feel is most probably the "click of death". The drive is effectively dead.

Just because fdisk can see the MBR (first 64 bytes -- of a 2 TB drive!) doesn't mean you will be able to mount it successfully, or get any data off of it. sdb1 is the NTFS partition you're looking for, but ntfs-3g is already telling you it can't read the NTFS signature (a preliminary step to mounting the drive).

I don't understand what you are attempting to do with sudo more /dev/sdb1?

You can try some "folklore" fixes that may or may not work, e.g. freezing the drive inside a ziploc bag for 24 hours to see if that temporarily fixes the problem, etc., but you should probably start resigning yourself to the fact that the data is most likely lost.