LIIs like to limit conversations to things they find interesting to talk about because we are poor small talkers and dislike having to shift our thoughts to the common mundane things people often use is a basis for socializing. My guess is she was probably waiting for you to mention something that crossed her interest. She might of interpreted you giving her space as, "Fuck it, you don't care about anything I'm saying so I'm just going to give up trying", which then prompted her in making amends by trying to restart the conversion. The secret to getting along with LIIs is all about finding out what they are really interested in, which can be a bit difficult because the interest of LIIs tend to be a bit distant from the mainstream things like sports, celebrities, relationships etc. LIIs usually only open up in talking about those interest once they feel they are in an atmosphere void of criticism and that they are unconditionally loved by whom they are speaking to.