....Should the part that houses the trip gear be wobbly ?
Quote....Should the part that houses the trip gear be wobbly ? NO
With the dial removed you should be able to pull the trip reset up and out, this will reveal a small screw accessed via the hole in the bracket by your red arrow. They often come loose.
Looking at back of speedo the cable drives it anticlockwise. If you look at the end of the cable and rotate back wheel the cable goes clockwise.
Just tested it with the drill in reverse .It bounces between 5 and 30, now stuck on 30.I will have to look up a repair shop and get it in the post. Roy.