Josephiah wrote (in separate messages):
0. I can only get it to add a gridline for every single entry, not just every half hour as I would like.
1. I eventually tracked this down to the fact that it doesn't like using data from the header column. Copying the exact same data to a non-header column made it work fine. Why on earth should that make a difference?
2. I can't format the line styles on the chart, only the symbol styles. With the 'Data Symbol' set to 'none' and 'Connect Point' set to 'straight', whatever I set the line style to, the lines remain resolutely 1-point solid lines of the default colour.
3. Now it won't let me label more than 10 points.
0.
Add the gridlines and ticks 'manually' using a Line shape with an end mark. Here's an example, using the image of your chart posted above. In practice, you would deselect the 'show gridlines' option in the Chart Inspector after placing the lines.
Downside: The gridlines are not attached to the chart. New ones will not be added automatically if further data points are added and the chart grows horizontally, nor will they move to maintain their position on the chart if the chart is resized.
1.
Header row and Header column cells are different from 'regular' cells in Numbers. Bar charts, column charts and other 'Category' charts use the contents of header cells to name each Series of values and to name each Category of data to be shown. If you select a Category chart, you'll see something like this on the Table feeding data to the chart:

The blue outline (and blue shading) mark the Data series that is feeding the chary. The white lettering on black background areas mark the Category names (Header column at the left) and Series name (Header row above the series data).
A Scatter Chart has no Categories. Each axis is a Value axis. Selecting a Scatter Chart shows a different diagram imposed on the Table feeding data to the chart:

Each point on the chart is determined by a Data Pair - an x value (shared in this case, and contained in column B) and a y value. Only the Header Row is used to provide labels for each series.
As a Value axis, the x axis in a Scatter chart has the same labeling and grid markers options as the y axis—you may specify up o 10 steps and choose to show the major grid lines (the grid line at each step) and from 0 to 10 minor gridlines, evenly spaced, between the major gridlines. By specifying a number of steps that would label only the hours, you could then show major gridlines plus 1 minor gridline to get a line at each half hour.
2.
Changing line colour and thickness is done in the inspector. The chart above uses none of the default line colours, several different data point markers and a connecting line thickness of 1 point. To change the line's thickness and colour, you must first select the line, not just the data point markers. Click on the line between two markers (if the markers are close together, you may find it useful/necessary to enlarge the view scale in order to select the line). When the line is selected, there will be small white circles between, as well as at, the data points.
Once selected, use the three Stroke controls in the Format bar to set the type of line (solid, dashed, dotted), thickness in points, and colour. The data point styles are set separately, in the Inspector.
3.
Category charts fit the labels automatically, and select as many as will fit from the list procided in the Header cells.
Value axes are limited to no more than 10 labels, set by the number of Steps chosen for that axis. Up to 10 equally spaced points between these 'major' axis points ma be marked with grid lines or tick marks, but not labeled.
Regards,
Barry