I believe the sort icon comes from the look. For example, in Windows standby mode, WindowsTableHeaderUI scans the following to draw the corresponding icon. For the upstream:
UIManager.getIcon("Table.ascendingSortIcon");
For descent:
UIManager.getIcon("Table.descendingSortIcon");
While BasicLookAndFeel registers a value for these properties (therefore, if you use a similar call, there may be something, as @Michael Borgwardt notes (drawing a conclusion from his answer), there is no guarantee of this, since any given appearance may prefer to abandon the UIManager and draw its own graphics.
However, it may be helpful to try to make it do what you need.
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