Travel to the council area in Vault City to speak with McClure, who will tell you that Randal in the Amenities Office has the part.
Now talk to Harry to learn of Gecko's radiation problem and they could use a hydroelectric magnetosphere regulator from Vault City to solve the problem. First pick up the part requisition form and other stuff from the desk behind him, for use later. You'll find Harold in the manager's office. The remaining ways, and possibly other minor quests I will leave up to you. Here is a list of some of the quests and other opportunities in Gecko, each with a brief synopsis containing at least one way to solve it. Either way, it's slightly northeast of Vault City, and is an area that's filled with mostly friendly ghouls and a few quests for xp worth earning.
Once you've been to Vault City and completed some of the quests there, you'll likely have Gecko on your world map.
