Seven Segment Scrolling
Python 2, 129 126 119 104 bytes



def f(n,k,p=0):z=p&lt;1or n&gt;0;q=-~ord('}/lx2Z^o~z'[n%10])*z;return(z and f(n/10,k,q))+k*bin(p^q).count('1')


Try it online!

Thx for a big 15 bytes from ovs.

As specified, takes a non-negative number and a positive sign length, and returns total changes.