when are the 'extras' (simanim) eaten at the seider, eggs and pomegranate?

Question

In my family, which follows the customs of Baghdad, it is a custom to eat eggs and pomegranate seeds during the seider. Problem is, nobody knows why, when and what to say.

I can see why the eggs are on the seider plate, such as discussed in this answer. None of my haggadoth mark the moment when these simanim should be eaten, and I could not find a commentary in our haggadoth about the blessings that should be used when introducing these simanim. I also could not find this custom discussed in the halachot of the Ben Ish Chai

What source discusses or was the base for the (babylonian jews'?) custom of eating the egg and the seeds of the pomegranates? What is the moment the egg and pomegranate are eaten and what blessing/text accompany them?

Answer 1

As you mention, possible symbolism of eggs are discussed in a different question and answer set, to which you linked.

As for pomegranate, this seems to me to be a likely allusion to the poles of pomegranate wood they used as a spit to roast the korban pesach. See pesachim daf 74.

We eat the egg at the beginning of shulchan orech. Absent any source to the contrary, I would assume a similar time for pomegranates. I don't know anything specific to say, but not everything needs a ritual text to recite.