The area you need to travel to, Arrapago Reef, is also the same area for unlocking Corsair. So you may want to start that quest as well: Luck of the Draw.
If you have access to Escape, you can take a shorter and much safer shortcut to Arrapago Reef. Go outside Nashmau's west gate from (F-10) to (E-9) Talacca Cove. Head generally north-east and you'll find a zone into Arrapago Reef. Cast escape, which will take you to (I-6) in Caedarva Mire, then go straight west to enter Arrapago Reef. Be warned that there are some undead and Lamia at night in the area you exit to.
A suggestion to try and obtain the Puppetmaster Job solo is to set your Home Point in Nashmau, then equip a Level 1 job, with a subjob which will provide Widescan. This will be useful in detecting Imps. You should be prepared by having a complete stack or more of Silent Oil and Prism Powder.
You do not need a Lamian Fang Key to reach the zone at (I-6).
Find the ??? at (H-10) on the first boat, hidden beneath the stairs, to receive a key item: Antique Automaton.
Return to Ghatsad (I-7) in Aht Urhgan Whitegate. Talk to him to give him the Antique Automaton. Wait for the next game day and talk to him again.
Return to Iruki-Waraki (K-9) to receive your Animator and to complete the quest. You will also be given a chance to pick your Automaton's name from a list.
Puppetmaster will not show up on your list of Job Levels until you zone.
