I would lean more towards the video wire right where it goes into the board. Also when you pull that board out, do it like this:
Add a little bit of solder to all the video connections...
Remove the new solder and it'll help pull all the old solder off too
Do 2 or 3 at a time so the whole connector doesn't fall out
Get nice new shiny solder on there and you should be fine. It's important to remove the old solder on these G07's... I tried in the past just adding a little bit of solder to reflow it, but on several monitors that made the problem even worse. If you remove the old solder, your problem will go away. Adding a tiny bit of solder first makes it easier to remove the old stuff.
It COULD be a neck transistor, or a pot but in my opinion that doesn't happen much on the G07's, the video connector acts up all the time on them so I'd go there first. Also since minor stuff makes it happen, it's more likely to be the wiring which is just hanging and easier to move, hence why moving the wheel, using the pedal, etc. vibrates enough to move the wiring slightly.