>>90426475Gachikoi is someone who is in love with their oshi, while a unicorn is someone who dislikes male-female interaction, though to what extent and whether it's limited to their oshi depends on the person. Many gachikoi are also unicorns, but you can be a gachikoi without being a unicorn or vice versa. Technically speaking neither needs to support their oshi to fulfill the definitions, but obviously most fans do in some way.
Btw gachizei (ガチ勢) is used to mean "hardcore fan", which is the closest to someone who just wants to support their oshi, but it doesn't exclude being a gachikoi or a unicorn.
Tl;dr you're right that gachikois that are not unicorns wouldn't care, but neither term means "someone who just wants to support their oshi".