Does isomerization occur by rotation about the central C-C bond?
Yes, rotation about a C-C bond generates conformational isomers.
Conformational isomers are structures that can be interconverted by rotations about single bonds. They are often called conformers or rotamers (rotational isomers).
For example, butane has both staggered and eclipsed rotamers.
The eclipsed conformations include a syn rotamer, in which the two CH₃ groups are closest to each other, and two enantiomeric (mirror image) rotamers with CH₃-H interactions.
The staggered conformations include an anti and two enantiomeric gauche rotamers.
Here's a video on the conformational isomers of ethane, propane, and butane.