In the description portion of flesh golem, I found this passage:
Elemental Spirit in Material Form. The construction of a golem begins with the building of its body, requiring great command of the craft of sculpting, stonecutting, ironworking, or surgery. Sometimes a golem’s creator is the master of the art, but often the individual who desires a golem must enlist master artisans to do the work.
After constructing the body from clay, flesh, iron, or stone, the golem’s creator infuses it with a spirit from the Elemental Plane of Earth. This tiny spark of life has no memory, personality, or history. It is simply the impetus to move and obey. This process binds the spirit to the artificial body and subjects it to the will of the golem’s creator.
Which would mean that the "soul" of a golem is actually an Elemental spirit. The Clay golem has the exact same passage, and Iron Golems talk of "the power of the elemental spirit bound within them".
So while the stat block for a golem in Construct, would spells and effects that target elementals also work on golems?