Her laying her head on his shoulder caught him by surprise. Ramirez hadn't received much physical contact since he arrived in Arcadia, and her doing this felt awkward to him. Though, it did remind him more of their time together at the Great Silver Shrine. She seemed to want to and need to keep her head there for some sort of comfort. So the silver-haired man let her.
Ramirez just sat there silently as Fina was laying her head on his shoulder, seemingly very distraught.