After the completion of Hunting the Archon, an email from Gil Brodie will arrive.
Read E-mail From Gil Edit
Read the email from Gil inviting Ryder to tag along to Eos and meet Gil's friend, Jill.
Acknowledge the email to obtain the next objective.
Meet Gil and Jill On Eos At Prodromos Edit
Head to Prodromos on Eos.
Ryder will speak with Gil about his friend Jill. Apparently Jill is on Eos to reverse the chemical procreation blockers given to all colonists. Gil crudely refers to this as "boosting the batter".
Depending upon Ryder's romance choices up to this point, Ryder may have the option to deepen the romance with Gil by sharing a kiss.
Ryder and Gil speak a little bit more about procreation (or their relationship) until Jill flies in on a shuttle and interrupts that part of the conversation.
Jill has noticed that Gil has changed for the better and believes Ryder has something to do with it. Depending upon whether Ryder is romancing Gil, the conversation with Jill changes but really is only about meeting and getting to know Ryder a little bit better.
The mission ends after the conversation is over.