Rulebook p118 on Factions.
"All units belong to one of the many Factions that are fighting in the 41st Millennium. This will often be represented on the unit's Army List Entry with a symbol, the key for which can be found to the right. A unit's Faction applies regardless of how you choose your army."
"Note that Fortifications are an exception in that, unless otherwise stated on their datasheet, they do not have a Faction."
The Tau Gunrig though, does have a Faction, because it has the Tau symbol on its datasheet (War Zone Damocles Kauyon p193). Next we will establish that they are models.
In Rulebook p8 Models & Units, the only language that actually defines what constitutes a model is the first sentence:
"The Citadel miniatures used to play games of Warhammer 40,000 are referred to as 'models' in the rules that follow."
It then goes on to say that models have nine different characteristics. Gunrigs are clearly Citadel miniatures, and since they are "Battlefield Debris (Gun Emplacement)" they have characteristics:
Rulebook p109 Battlefield Debris
"A gun emplacement can be shot at and attacked in close combat. It is hit automatically in close combat and has the following profile: S- T7 W2 Sv3+.
This means they meet the demand for being models. There is a counter-point:
Rulebook p9, Zero-Level Characteristics
"Some creatures have been given a 0 for certain characteristics, which means that they have no ability whatsoever in that field (the same is also occasionally represented by a '-')."
"If at any point, a model's Strength, Toughness or Wounds are reduced to 0, it is removed from play as a casualty."
This is the only suggestion I can find that Battlefield Debris are not models, since they have 0 Strength but aren't immediately removed from play. However, guns in Artillery units have the exact same stat line (Rulebook p64), are referred to as models, and are not immediately removed from play either.
Furthermore, the sections "Allocate Wounds & Remove Casualties" in Rulebook p51 and p35 only speaks of allocating wounds to models, and reducing the Wounds of models by 1, and removing models as casualties if their Wounds reach 0. Therefore, if Gun Emplacements are not models, they cannot be removed as casualties, and I think that has to count as the more absurd interpretation.
Therefore, Gunrigs are non-vehicle models with the Tau Faction and can have wounds allocated to them.
And now, the entire point of the thread.
Tau Codex p76, Invocation of the Elements.
"The Ethereal, and all friendly non-vehicle units with the Tau Empire Faction within 12" benefit from the effects of the elemental power until the start of the Ethereal's next Movement phase."
Rulebook p164, Feel No Pain
"When a model with this special rule suffers an unsaved Wound, it can make a special Feel No Pain roll to avoid being wounded"
Since Gunrigs meet the requirements of Invocation, and are able to suffer unsaved Wounds, they should get a 6+ FNP from the Sense of Stone elemental power.