A relatively short but excellent video demonstrates the comet's movement from night to night and shows the difference not having a bright moon in the sky makes. One might think, naively, that the comet's trail indicates the direction it's moving, but this isn't the case. It shows the direction of the solar wind. There is an anti-tail, which I couldn't see for certain in this collection, that does trail the comet, but it is made up of fewer larger dust and ice particles that aren't affected by the solar wind compared to the ions streaming of the comet, which create the bright trail.
https://youtu.be/CctFLzGqMJo?si=Z4R2pDp1tjK1buBz
PS. Looking back at the video, the anti-tail might be briefly visible at the 02:36 mark and possibly again at 02:56 (look right below the comet). The video is noisier because the ISO/gain has been turned up, so there's no way I'd claim this is real, but it's where you'd expect the anti-tail to be. Watch the video at half or quarter speed at those times, and you might see what I do. Incidentally, you can also see Venus' motion throughout the whole video.
https://youtu.be/CctFLzGqMJo?si=Z4R2pDp1tjK1buBz
PS. Looking back at the video, the anti-tail might be briefly visible at the 02:36 mark and possibly again at 02:56 (look right below the comet). The video is noisier because the ISO/gain has been turned up, so there's no way I'd claim this is real, but it's where you'd expect the anti-tail to be. Watch the video at half or quarter speed at those times, and you might see what I do. Incidentally, you can also see Venus' motion throughout the whole video.