The line that offers an indirect characterization of Billee is:
“Billee wagged his tail appeasingly, turned to run when he saw that appeasement was of no avail, and cried (still appeasingly) when Spitz's sharp teeth scored his flank.”
This line illustrates Billee's gentle and submissive nature through his actions of wagging his tail in an appeasing manner, attempting to avoid conflict, and expressing distress when attacked. It shows his character traits without explicitly stating them.