Thanks for the long explanation.  I am using the 2014 version of
gnuplot-mode and gnuplot 5.2. 

gnuplot-mode has a customizable variable, gnuplot-program, which
specifies which command to execute to start gnuplot.  The default value
for this variable, at least in the 2014 version, is simply "gnuplot" so
it will pick up the default gnuplot on Linux (if there is more than one
version installed, I imagine that /etc/alternatives will be used to
identify the default).

If you think the wrong gnuplot is being picked up, maybe customize this
variable?  What do you get if you simply invoke "M-x run-gnuplot"?

--
Eric S Fraga via Emacs 27.0.50, Org release_9.2.3-327-g3375f0