If you do something "in time" with music, you make your feet/body move to the same rhythm as the music. If there was music playing, and the speaker and their girlfriend were both "mincing" (a very stylised way of moving) to the same rhythm as the music, they could be said to be "mincing in time".
I agree with emsr2d2. I would also suggest that if he was mimicking his girlfriend by mincing along at the same tempo as her, then he could be said to be mincing in time with his girlfriend even if there was no music present.
[FONT="]A walking tour should be gone upon alone, because freedom is of the essence; because you should be able to stop and go on, and follow this way or that, as the freak takes you; and because you must have your own pace, and neither trot alongside a champion walker, nor mince in time with a girl.[/FONT]
I am sorry about that. I happened to read this portion in a web-page which discuss it as an example. I didn't know it was very old. I thought it may be something common to use in English.
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