Definition of "insistence"

He made gourd-rattles (known in ever so many parts of the world) in which he rattled dried seeds or small pebbles with a most beguiling and rain-like insistence[.]

1920, Edward Carpenter, Pagan and Christian Creeds, New York: Harcourt, Brace and Co., published 1921, page 72

The extreme depth of these channels, and the insistence of the Board of Trade on a headway of 150 ft. for the unrestricted passage of large ships, necessitated a high bridge with two main spans, and a central pier on Inchgarvie.

1950 March, H. A. Vallance, “On Foot Across the Forth Bridge”, in Railway Magazine, page 147