Sorry, there was some debugging cruft in the previous patch.  New one attached.

(file #42156)

Wait for me to confirm that patch.  I'm trying the example in

https://savannah.gnu.org/bugs/?52186

right now and that seems like the exact same issue, i.e., the arrows are being remembered between plots.  There may need to be a second location where the arrows are cleared...

There looks to be multiple issues with the following:

graphics_toolkit gnuplot
figure
plot([0:50], sin(0.03*pi*[0:50]), 'b');
set(gca, 'xcolor', 'b');
set(gca, 'ycolor', 'b');
set(gca, 'box', 'off');
ax = axes('Position', get(gca, 'Position'));
plot(ax, [0:75], 2.5*cos(0.03*pi*[0:75]), 'r');
set(ax, 'xaxislocation', 'top');
set(ax, 'xcolor', 'r');
set(ax, 'yaxislocation', 'right');
set(ax, 'ycolor', 'r');
set(ax, 'color', 'none');
set(ax, 'box', 'off');

1) The two axes don't align even though I specified they should have the same position.

2) There is a vestigial blue border for the second plot when I specified box off.  It's odd that the following doesn't have that border:

graphics_toolkit gnuplot
figure
plot([0:50], sin(0.03*pi*[0:50]), 'b');
set(gca, 'xaxislocation', 'top');
set(gca, 'xcolor', 'b');
set(gca, 'yaxislocation', 'right');
set(gca, 'ycolor', 'b');
set(gca, 'color', 'none');
set(gca, 'box', 'off');