Following command only shows 6 data points instead of 8 in gnuplot 6.0.3 patchlevel 3:
gnuplot -e 'set term dumb size 60, 20' -e 'plot "-" u 1:2 t ""' << EOF
0.0625 0.019509
0.1875 -0.055557
0.3125 0.083147
0.4375 -0.0980785
0.5625 0.0980785
0.6875 -0.083147
0.8125 0.055557
0.9375 -0.019509
EOF
Adding -e 'set yrange [-0.11:0.11]' before plotting shows 8 data points.
As you say, increasing the range shows that in fact all 8 points are present. Since auto-scaling uses the extreme point coordinates to define the border, and the border of the plot is by default drawn after the points, it covers the two points with extreme coordinates. Try again with
set border backto confirm.