After creating the initial scatterplot from the table above (using Graph/Scatterplot Matrix), right-click on the graph and select "Row Legend". This dialog box appears:
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Select "Color" and JMP automatically assigns colors to the categorical variable using "JMP Default" setting in the colors pull-down option. This can be changed but I left it as-is. Note that Markers is pre-selected as "None". I left this as is. Pressed ok.
On the resulting graph, I again right-clicked and selected "Row Legend". And I see this:
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When I click on "Shape" under columns, note that JMP assumes that I want to use this column to again assign a color. I have to do two things. First, I have to select a marker scheme from the "Markers" pull-down menu. I chose "Solid" like this:
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Then, for the most important step, I have to click on the Colors menu and change the pre-selected JMP Default" option to the "None" option which is "hidden" all the way at the top of the pull-down menu. Here:
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Then click on ok. To get the final graph with two legends.
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This is what I want.
The combination of the pre-selected Color menu-item and the "None" hidden all the way at the top cost me hoursOfFun (mostly searching through documentation and posts). Maybe this dialog box needs a bit of tweaking. It's the same that is under "Rows/Color or mark by column . . . " so it's a fairly important bit of kit.
Hope this helps someone else save some time.