Driver 100% moves first.
In this video there are 10 frames per second so the timing here, the first bit is seconds into the video, last bit is frames which is 1/10th of a second, it's not milliseconds.
Driver move forward twice, first at 31:03 - 31:07 secondly at 32:07-33:00. The teacher starts to sit on the bonnet at 33:07, ~7/10ths of a second after the 2nd move forward.
I've exported these frames from After Effects using a mixing mode called "difference". Difference is a common photoshop layering method - what it does is if the top layer is black, it has no effect and you just see the bottom layer, if it's white then the bottom layer is inverted. In between black and white, or coloured and you get a partially inverted or coloured image. It's what designers use when they are making things like this:
With video, by offsetting a second layer of the same video by one frame and using the difference mixing mode, what you get is an output which only shows where the image has changed. If there is no difference, the image is black. So by doing this I can find movement. It's pretty faint tbh but it is clear. You can see the effect clearly in the cars behind which move alot. This driver has nudged forward so it's only faint but hopefully you can see it.
I tried uploading them all to imgur but it only accepted three of them and it's renamed them so I can't be 100% sure which frame is which but I think the top one is from 31:02, before the driver moved so you can see what it's like. The second one is during one of the movements - you can faintly see the outline of the front of the car. I think the last one if from when he starts to sit down.
edit: forgot the imgur link
edit 2: there's 6 images, not 3 as it showed me in the preview
I could post the export here (AE names them automatically with the frame numbers) but it'd be quite a few images and a fair few mb, let me know if you would like me to.