One way would be to figure out the necessary information of the respective planet from the output of
Entity["Planet", "Earth"]["Properties"]
But if you just want this connecting line, it it probably easier to use some kind of "reverse engineering" and do it simply like so:
ssp = ResourceFunction["SolarSystemPlot3D"][{Blue,
Sphere[Entity["Planet", "Earth"], 0.05], Red,
Sphere[Entity["Planet", "Mars"], 0.06]}, PlotRange -> 1.8,
ViewPoint -> Above, Boxed -> False, "IncludeSun" -> True,
"IncludeReferenceObjects" -> False, "SunStyle" -> {Hue[.14],
Lighting -> {{"Ambient", GrayLevel[.3]}, {"Directional", White,
ImageScaled[{0, 0, 1}]}}, Sphere[{0, 0, 0}, .1]}];
connLine = Line[Most@Cases[ssp, Sphere[pos_, rad_] :> pos, Infinity]];
Show[ssp, Graphics3D[{Dashed, connLine}]]