Brigh is, according to the Pathfinder Wiki, the goddess of invention, and it seems that any construct that could be considered "alive" is of particular interest to her.
On the other hand, Flesh Golems (like Frankenstein's monster) are more like an assembly of body parts sewed together, which seems a lot like necromancy. Still, Flesh Golems are "Constructs".
Question: Are the "more organic" constructs like Flesh Golems, Alchemical Golems, or Homunculi included in the list of the constructs favored by Brigh?
Best Answer
Probably yes, but she has more favor for inorganic constructs.
There's a chapter about Brigh in Inner Sea Faiths, and another chapter in Lords of Rust, the 2nd book of the Iron Gods adventure path. Nothing in either chapter suggests that inorganic constructs are outside of the Brigh relgion.
Superficially, Brigh is the patron goddess of clockwork, machines, and metalwork. There is lots of evidence for this.
However, whenever these sources mention how Brigh cares for constructs, it never specifically says that the constructs must be mechanical or inorganic. There is plenty of evidence that Brigh is the patron goddess of all constructs, even if the materials themselves are organic.
According to Inner Sea Faiths, Brigh is described as "a patron of all invention". That's a large category, and should include both organic and inorganic inventions.
Clerics of Brigh can prepare Unbreakable Construct and Control Contruct (page 32). Both of those spells have a target of "one construct", and nothing about the spell text indicates that the target must be metallic.
I only found one mention of flesh golems, located in the "Planar Allies" subsection (page 33):
First, note the word "perfect" when describing inorganic constructs. This strongly suggests that Brigh favors mechanical creatures above others.
Still, it's plausible that if one of Brigh's divine servants is known for overseeing flesh golems (and similar alchemical constructs), then those types of constructs should also be within the realm of Brigh worship.