The location is random, and the "Suspicious Object" moves to a different spot after a while, but we may as well keep track of the places where we found one "Suspicious Object". I just waited at a spot and clicked it when it appeared, saves you some walking around.
(J-11) Directly in front of the Entrance to the Mog House.
(E-9) just before bridge to where present Cooking Guild sits
(F-5) on the pathway to Sarutabaruta
(F-7) by canon blast in ground
(F-8) on top of the Optistery
(G-7) by the Home Point crystal
(G-8) infront of the Optistery door
(G/H-8) on the stairs
(H-8) of south Waters
(K-10), In front of the wall to the Residential Area
(K-10) On pathway to Residential Area
(L-6) on top of east Aurastery building
(L-10) In the middle of the clearing in front of Mog House Area
(L-11) Right near Pettette in front of Mog House entrance
All "Suspicious Objects" are pooled, meaning if multiple people undertake the task at the same time, they all can see the same points. This can lead to competition over spawns.
"Suspicious Objects" can respawn in the same place multiple times in a row.
"Suspicious Objects" will not show up on the Job Ability Wide Scan
"Suspicious Objects" will despawn if unclaimed 2-3mins after spawning.
It is possible for more than one "Suspicious Object" to be up at the same time.
Yagudo spies have infiltrated Windurst and planted instruments of mass destruction and/or mayhem (IMDaoMs) in various discreet locations. You are to patrol the capital and remove any hazardous materials you encounter.