Stephen had said "we need to find them", Gideon had countered with "the new Kindred of Sacramento need to". Normally Headstrong would side with Gideon, but in this instance... Gideon was just not used to dealing with the less philosophical and more direct threats to the Order. But that hardly mattered; that was her job anyway.
Headstrong decides to say or betray nothing for now. Her companions had been with her long enough to sometimes understand her even if she withheld all visual cues and there was no reason to rush this matter. Headstrong would rather be safe than sorry.