A hen does not need a rooster around to go broody. She does not need eggs, fake or real. It’s a hormonal thing but I don’t know what triggers the right hormones.
There are certain signs that a hen might be broody. They might spend a lot of time on the nest. They might be very defensive of the nest, fluffing up and growling at you if you come near, maybe even pecking you. A broody normally leaves her nest once or twice a day to eat, drink, and poop. When they are off the nest they usually walk around fluffed up and making a pukking sound. They just look and sound mean.
I’ve had hens do all or some of that and not be broody enough to give them eggs. Some you can pretty well tell they are broody when you just see them, but some can occasionally fool you.
My test to see if a broody is worthy and committed enough to give eggs to hatch is that she has to spend two consecutive nights on the nest instead of roosting in her favorite spot.
I had one yesterday walking around fluffed up and making that pukking sound, but she was in the roost last night when I locked up. She was not on the nest this morning when I let them out. She was just teasing me.