E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
To sit on the rail. To shuffle off a direct answer; to hedge or to fence; to reserve the decision of ones 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 again.T. Terrell: Lady Delmar, chap. i.