Martykl,
To finally answer the question, was there 'any Parker solo, specifically that made me think that', NO.
As is usually the case, it's the 'body of work', the style, the simple phrasing, repeated 'licks' that a player uses that become his signature (maybe her).
I just noticed, not at the time, as I was 12 when 'Can't Get Started' on the Cannonball/Wilson Album, came into my consciousness--that they share similar licks and phrasing, and since Cannonball came after Parker somewhat, one would have to conclude that he was influenced greatly by his omnipresent works. Just as, one doesn't have to be a music critic to hear Clifford Brown's influence on Chris Botti's work.
Overall, I'm more of an Adderley fan than Parker, but primarily because of the Be Bop of Charlie's era, which predated me somewhat. Cannonball was MY contemporary and I grew up with that--plus the subtlety of Cannonball's tone is overall, more to my liking.
How, given their collective, enormous tallent can we not love both?
Again...it was the overall Marty, the whole not the specific that led me to that statement, and of course, as usual, I'll say that I'm probably mistaken.
Good listening,
Larry