External drive wont mount

Erase it and reformat it, if it doesn't work, I'm sorry to say that your HD may be dead.

"What would be the next troubleshooting step to mount or recover this drive?"

Here's what I did when I was in a situation similar to yours. I had a drive with a partition on it that would no longer mount. Unfortunately, that partition had the data that I wanted on it (many hundreds of mp3 files).

Even data recovery software (I was using Data Rescue) couldn't "touch" it, because it wouldn't mount and DR couldn't access the unmounted partition.

My solution:
1. I first re-initialized the drive into a SINGLE partition (but I -DID NOT- choose to "zero out" the drive)
2. The drive was now "mountable" -- even though it showed that "nothing" was on it, no contents!
3. I then launched Data Rescue and "attacked" the (so called) empty drive. DR "ignored" the drive's [new] directory and went "right to the platters" -- and FOUND the old file data which was still there (because I didn't zero out the data, remember?). It then scavenged the data from the drive sectors and re-assembled it and saved it onto a second "scratch drive".

This scenario -MIGHT- work for you if nothing else does. No promises. But before you give up on the drive, it could help you get some of the data back.

What you will need:
1. A SECOND drive -- yes, you'll have to buy another one. I recommend that you get a USB3/SATA "docking station" and a "bare drive", instead of a pre-assembled external.
2. Data recovery software, such as "Data Rescue 3" or "Stellar Phoenix Data Recovery".

It will take some time, some money, and an effort to learn on your part. There is no way around this.

Also, be aware that even when data recovery is successful (as it was for me), you will probably lose most (if not all) of your file names, and you will also lose any pre-existing folder hierarchies. These were "constructs of the directory", and to get at the data, it was necessary to replace the old directory with a "fresh" one (when you re-initialize).

DO NOT DO NOT DO NOT "zero out" when you re-initialize! This WILL "wipe out" any chance of getting the data back!

One other thing to be aware of: if your drive has experience an actual hardware failure, such as broken drive heads, the above process won't work. It's only for when the directory structures have been damaged (soft failure). When a drive has a hardware failure, it usually has to be taken apart before there can be any recovery -- an expensive operation.

+1.....

for Fishrrman and the procedure outlined. I use some like that with a problematic SD card damaged by a stupid PC. But I used Stellar Phoenix, Mac edition.

I was able to recover all the info. But takes a lot of time (and was a 16 GB SD card, pal...!)

So, give it a try if the info is valuable for you. Otherwise, think about the HDD as dead....