Writing Solo's

Not necessarily only guitar solo's, but any instrument solo that is recorded to highlight your ability (please don't think I mean just technical prowess). 
I attached a short video trying to highlight a process I experienced the other night writing a guitar solo for an original tune. 
With no preconceived notion of what to play or when to play the notes, I just hit record to lay down whatever comes to me in that moment, and when I listened back, it just struck me that I found the right melody and feel in that first take. Have you experienced this before? Something about the way notes/tones/rhythm interact with a backing track just seems it was meant to be? It's interesting trying to go back and recreate that moment, e.g., the electric guitar part in the video. Please feel free to discuss how you write a solo and provide some media highlighting the solo. 
 
https://www.youtube.com/watch?v=A-TWUyrl-Pw