In order to avoid special relativity (explicitly), picture a coil with a current running through it. It generates a magnetic field perpendicular to the direction of the current (say, in parallel to the opening of the coil). Think of a very big coil with the rod moving towards one of its walls. Now, a moving rod that interacts with such magnetic field will get an emf induced because the charges inside it are moving perpendicular to the field and so they are forced to move perpendicular to those directions.
Here comes the fun part. A frame of reference where the magnetic emf is zero, is one that is moving with the charges in the coil that generates the magnetic field. So basically, rotate the plane in which the rod exists at an angular velocity that matches the one of the charges in the coil (the current). In this frame, the rod is moving in an outward spiral. The electric interactions are then towards the wall and won't contribute to the emf. Why would there be an emf induced then? The charges on one side of the rod will experience more force as what used to be a constant velocity is now an always changing acceleration (since the rod is rotating around the origin, moving outwards, and changing the direction it faces). Since both ends of the rod experience different accelerations (one always going in, the other out), because they have to constantly face the wall, a force gradient (difference) is induced. More importantly, since the angular velocity of the rod is constant, the orbital velocity of the rod must increase with the radius. Therefore the rod is being accelerated in a direction that's more aligned with one side than the other, this force acts on the individual charges, creating the flow of current. Space generates the force on the charges in this frame of reference.
I hope this helps!