My standard bronze hen had gender issues until I got her a boyfriend. She would strut and display and her head would change colors. This all stopped though when she got her boyfriend.
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I went out and took some pics this afternoon to try and get them side by side where the differences are more apparent. Here is the best pic I got to illustrate:
The tom is on the left. As you can see, the dangly bit under his neck is larger and curves round/down whereas the hen's is smaller and not rounded. You can also see how much more black he has. Since I only have the two, I don't know if this can be explained by individuality but do have a friend with RP's who commented that her toms have more black so I think perhaps it does indicate gender difference.
Regarding gobbling, mine mostly does not gobble when I go to see him. I am part of the scenery and not worthy of such attention apparently. But when I take someone new down to visit, that is when he will start gobbling like crazy. Renee, perhaps a friend or family member they aren't familiar with, could go and visit with you and see if any of the toms start up then?