Graysexual
Somewhere between asexual and not — attraction that's rare or conditional.
Graysexual describes people who sit in the grey area of the asexual spectrum. They do experience sexual attraction, but rarely, faintly, or only under particular conditions.
Some feel it a handful of times in their life. Some feel it only after a deep bond has formed, which overlaps with demisexual. Some feel it but have no wish to act on it.
The word exists because asexual and allosexual, taken as a binary, leave a lot of people with no accurate way to describe themselves.