If a Quaker says she is waiting for the Spirit to move her to speak, to find some ministry for the Meeting, I take that to have some relationship to a sense of God, of a power beyond human dimensions. Possibly but not necessarily to a supernatural entity.
Her own feeling may simply be of something greater than we can know, of something within each of us, of...well, perhaps it's better left as a general term covering an intense communication with, er...
OED: "Spiritual: having a relationship based on a profound level of mental or emotional communion." Whatever the relationship might be, and with whoever or whatever the communion might take place, I can run with that.
Spirit: (OED) "the non-physical part of a person which is the seat of emotions and character; the soul." I can't see that there is a non-physical part of a person, in the sense of a supernatural entity, and the word "soul" is the problem here, because for me it relates back to the fairly traditional and conventional Christianity of my school days. But there may be a universal common self, the Light within us that we all have, a self below and beyond the ego.
When Gautama Buddha was close to death, he didn't tell his followers to believe in him and he would lead them to the Father, so they would be saved. He simply said that each of them had to light his own lamp.
That individual light may relate to a "spiritual path" that could chime with Quakers and Buddhists.
But the Tao Te Ching reminds us right at the start that
"A way that can be walked
is not The Way
A name that can be named
is not The Name.
Tao is both Named and Nameless."
To reach a profound sense of communion beyond the ego, we have to break through the frame of either/or, of comparisons and polarities, of conceptual analyses. I think that's valid whatever your "spiritual path." There's only so much we can do with ordinary speech and writing. The rest, the other, may involve being in silence for a while.