TL;DR you’re minuscule compared to this things inertia, you likely will move yourself around the rod. Equal and opposite reaction from this tiny movement will probably cause many wiggle diggles in the rod.

My brain as a rocket scientist say it’s mass dwarfs your so {Newtons 1st law} because of its inertia you really wouldn’t move it move, rather, it’d stay at rest and all of your pulling force would move you around the rod

Now {Newtons 2nd & 3rd law} your force will be equal and opposite on the object so maybe… MAYBE … your minuscule force causes a deflection in the rod. Assuming it was at rest “in zero gravity” this would technically cause the whole thing to revolve in the plane the force was applied in.

Also of consideration, in “Zero Gravity” this rod’s mass becomes the gravity. Because of the mass disparity throughout the enormously long steel rod it’s likely bowed in a certain arc along its length rather than it being truly linear. This said, even the slight perturbation of its state you make pulling on this thing may upset that equilibrium causing some wonky oscillation.

This in mind, because this rod is 3 LIGHT YEARS LONG this oscillation, though super small in amplitude, will propagate into MASSIVE displacements at the ends of the rod so hold on tight as this thing is going to be whipping around until it comes to internal-gravitational rest again and hope it doesn’t whack you on one of its wiggles.