To sit on the rail. To shuffle off a direct answer; to hedge or to fence; to reserve the decision of one's vote. Here rail means the fence, and “to sit on the rail” to sit on one side. A common American phrase.
“If he said `Yes,' there was an end to any church support at once; if
`No,' he might as well go home at once. So he tried to sit on the rail
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894