I don't personally believe in a "core sexual orientation" because I don't particularly believe in sexual orientation in the first place. My sense is that we're culturally indoctrinated to believe there's a "spectrum", and we therefore must have a "position on it", simply because that's how we tend to think about things: fixed, quantifiable, digital. There's so much unnecessary suffering caused by people having to wonder "what am I?" instead of just being attracted to individual people at the time and not needing a word for it.
Over the years, my "orientation" has, like Jenny's, wandered about like a pilgrim, dependant on... what? Who knows. So many possible influences that might lead to me having, at a particular time, a particular tendency more towards men or women or celibacy or or or. Some of it emotional, some of it cultural, some of it psychic, some of it biochemical, interesting to speculate, impossible to know all the conditions. I've totted up the over 80 people I've fallen for over the years, and they come down pretty much 50/50 men and women, but that's over an almost 40 year period. Right now I have a new attraction to (in my perception) straight-looking men, which has replaced my previous interest in androgynous pretty-boys, but I'm still very attracted to wiry dykey gals. And then I fall for someone, and it's because of their smile more often than anything else.
I've mostly identified myself as bisexual in the past (except when I was pretending to myself I was gay, in order to cover up that I was running away from women), but since I actually started meeting other transgender/androgyne people, it feels much more sensible to call myself polysexual, in that first I'm attracted to someone, and then find out what they're nominal gender is, and I'm realising these days you can't assume someone's gender or gender identity from outward appearance.
And if I'm attracted to someone, I'm much more interested in whether they fancy me back than what they identify as! After all, there's no advantage in being (for example) a bi woman attracted to a gay/bi woman or a straight/bi man, if they're not attracted to me! It's always made me laugh with frustration in the past when I've told a guy I fancy him, and he's said "sorry, I'm not gay..." instead of just saying "sorry, I don't fancy you."