It means that when they do cast politics a fleeting glance that moment will supply their reasoning.
Times, Sunday Times
Well, not judging from a fleeting glance at the first-quarter figures: a 764 million attributable loss (report page 45).
Times, Sunday Times
One fleeting glance behind him and he struck out.
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We exchanged fleeting glances of mutual dislike and incomprehension.
Times, Sunday Times