And even if it did, it will set the background for the whole equation.
Mr Cwikel wants to have a different background for each part of the
equation.

Each part? I do not see that from the orignal post.

 have those little corner markers remain visible atall
times, perhaps changing to a different more intense colour when the > cursor is 
inside the particular region that they enclose.

This is easy. Can I apply this?

Index: src/insets/Inset.cpp
===================================================================
--- src/insets/Inset.cpp        (revision 18242)
+++ src/insets/Inset.cpp        (working copy)
@@ -287,7 +287,7 @@
void Inset::drawMarkers(PainterInfo & pi, int x, int y) const
{
       Color::color pen_color = editing(pi.base.bv)?
-               Color::mathframe : Color::background;
+               Color::mathframe : Color::mathbg;

       int const t = x + width() - 1;
       int const d = y + descent();
@@ -302,7 +302,7 @@
void Inset::drawMarkers2(PainterInfo & pi, int x, int y) const
{
       Color::color pen_color = editing(pi.base.bv)?
-               Color::mathframe : Color::background;
+               Color::mathframe : Color::mathbg;

       drawMarkers(pi, x, y);
       int const t = x + width() - 1;

Cheers,
Bo

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