In order to get to the Ether Mine, of course, you have to actually use the lift to go down. Remember that after you hit the Call Button and get on, you have to also operate the Lift Button on the lift- this may take a little camera finagling to find, depending on how you approached the lift. Once you’re down, you’re in a new area- the Broken Path. This region is very hazardous- it’s a series of thin land bridges that, in defiance of physics, jut out a few score meters from the side of the Bionis and interlace, and there are no railings of any sort anywhere. Go slowly and watch your step- and make sure you’re high enough level that the monsters here cannot panic you. If they do, you’re going over the edge, and then you have to start all over at the entrance to the region.
Fortunately, most of the monsters here are spaced out. The Sky Rhogul are destined to cause you trouble if you’re low enough for them to sight-aggro you, so stay attentive.
You also want to make sure you head towards the cliff face every time it’s possible- not only is there an Electric Ether Deposit here, but Daza’s missing Nopon Coin is near the cliff face on one of the land bridges, and you want the rewards from his quests.
If you haven’t managed to complete the area’s Collectapaedia page yet, make sure you walk- not run- out onto the very tips of the land bridges as well- Collectable items like to spawn and lurk there, tantalizingly close to a fatal fall.
Daza’s second quest requires you to fight the Antol and Upa that are found on these bridges as well, and you’ll want to be careful about that also- Upa pack a knockdown attack that, if poorly timed, can leave you falling on your back into the water from uncountable kilometers up. Fortunately, you’re overlevel to these things (you -have- been doing most of everything, at least, up till now, right? If not, you may well find yourself regretting it inside the mine.). This is a good chance to get some practice in with maneuvering in restricted spaces- you’re going to have to deal with walls and confinement within the mine, which is in a sense the mirror match to the floorless drops that you have here, and the monsters in there are much more threatening.
As an additional note, by this point you should at least have all of the Arts that you tend to use leveled up to II rank, preferably up to III rank if you can afford the AP. Furthermore, you should take this opportunity to go back to Colony 9's Ether Forge and forge all the gems you want at rank I (and occasionally Rank II). After this virtually all the crystals you’re going to get, from deposits and otherwise, are Rank II Large crystals, and you can’t combine crystals or cylinders if they’re of differing ranks. Or sell them. Either way, you should empty out your Ether Crystal/Cylinder inventory tab of all thsoe Rank I things to make space for the more powerful and more useful Rank II stuff you’re going to fill up on in the mine.