Unusable 2.5" external HDD. Partition failed with the error -69760: Unable to write to the last block of the device. Exfat only? Repairable?
As per @bmike's suggestion. I'm putting my attempts at solutions in this answer to avoid repeatedly bumping the comments section and to clean up the original question.

As per @Allan's advice I formatted the drive to Exfat on Windows, although the "format did not complete successfully". On Disk Utility I now can see a greyed-out volume named Disk1s1. However, I still get the message, "The disk you inserted was not readable by this computer." "[Initialize | Ignore | Eject]", when connecting to my MBP. Moreover, the 'First Aid' option in Disk Utility is greyed out.

Now, diskutil list command result gives a volume type of DOS_FAT_16. Compare this with the previous results that shows the original (working) and previous (unusable) states. 

The disk currently does not work on Mac or Windows.
Next steps from here?

--

Currently the disk is unusable but with greyed-out disk1s1 in disk utility. /dev/disk1 gives:

   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     FDisk_partition_scheme                        *2.0 TB     disk1
   1:                 DOS_FAT_16                         2.0 TB     disk1s1


sudo gpt -r -v show disk1 gives:

gpt show: disk1: mediasize=2000398934016; sectorsize=512; blocks=3907029168
gpt show: unable to open device 'disk1': Input/output error


sudo diskutil verifyDisk /dev/disk1 gives:

Unable to verify this whole disk: A GUID Partition Table (GPT) partitioning scheme is required (-69773)


diskutil info /dev/disk1 gives the following:

   Device Identifier:        disk1
   Device Node:              /dev/disk1
   Part of Whole:            disk1
   Device / Media Name:      JMicron Generic Media

   Volume Name:              Not applicable (no file system)

   Mounted:                  Not applicable (no file system)

   File System:              None

   Content (IOContent):      FDisk_partition_scheme [PREVIOUSLY THIS WAS "NONE"]
   OS Can Be Installed:      No
   Media Type:               Generic
   Protocol:                 USB
   SMART Status:             Not Supported

   Total Size:               2.0 TB (2000398934016 Bytes) (exactly 3907029168 512-Byte-Units)
   Volume Free Space:        Not applicable (no file system)
   Device Block Size:        512 Bytes

   Read-Only Media:          No
   Read-Only Volume:         Not applicable (no file system)
   Ejectable:                Yes

   Whole:                    Yes
   Internal:                 No
   OS 9 Drivers:             No
   Low Level Format:         Not supported


Previously the results were:

Nonexistent, unknown, or damaged partition map scheme
If you are sure this disk contains a (damaged) APM, MBR, or GPT partition
scheme, you might be able to repair it with "diskutil repairDisk /dev/disk1"


diskutil repairDisk /dev/disk1

Nonexistent, unknown, or damaged partition map scheme
If you are sure this disk contains a (damaged) APM, MBR, or GPT partition map,
you can hereby try to repair it enough to be recognized as a map; another
"diskutil repairDisk /dev/disk1" might then be necessary for further repairs
Proceed? (y/N) y
Error repairing map: POSIX reports: Input/output error (5)


diskutil partitionDisk disk2 1 GPT JHFS+ "Untitled" 100%

Started partitioning on disk2
Unmounting disk
Error: -69760: Unable to write to the last block of the device


Here's what I've had a look at (but not sure if it applies to my case):

http://www.macissues.com/2014/04/05/how-to-fix-deep-formatting-problems-with-os-x-drives/ (I attempted cat /dev/random &gt; /dev/disk1 once only, but got a stdout: Input/output error response)

https://ipfs-sec.stackexchange.cloudflare-ipfs.com/apple/A/question/125965.html (I tried diskutil eraseVolume exfat exfat2tb /dev/disk1 but got the following:

Started erase on disk1
Unmounting disk
Erasing
newfs_exfat: 
wipefs_wipe: Input/output error
Volume name      : exfat2tb
Partition offset : 0 sectors (0 bytes)
Volume size      : 3907029168 sectors (2000398934016 bytes)
Bytes per sector : 512
Bytes per cluster: 131072
FAT offset       : 2048 sectors (1048576 bytes)
# FAT sectors    : 120832
Number of FATs   : 1
Cluster offset   : 122880 sectors (62914560 bytes)
# Clusters       : 15261352
Volume Serial #  : 5ec6682e
Bitmap start     : 2
Bitmap file size : 1907669
Upcase start     : 17
Upcase file size : 5836
Root start       : 18
Mounting disk
Could not mount disk1 with name (null) after erase
Error: -69832: File system formatter failed


Previously (unusable disk):

       #:                       TYPE NAME                    SIZE       IDENTIFIER
       0:                                                   *2.0 TB     disk1


Originally (working disk):

       #:                       TYPE NAME                    SIZE       IDENTIFIER
       0:     FDisk_partition_scheme                        *2.0 TB     disk1
       1:               Windows_NTFS                         2.0 TB     disk1s1