Others have provided excellent answers explaining both regular tugs and gravity tractors. So let me add a justification of my "1st rule".
It boils down to the fact that in space you can, with a very good degree of approximation, determine the trajectory of an object not under thrust, knowing only these two things: it's position at a given time, and it's velocity at that same time. These two vectors give you a single trajectory through space.
It follows from two physical laws that you may remember from high school:
- Newton's second law, or F=ma
- Newton's law of universal gravitation, or F=GMm/r^2
If you put them against each other, you get ma=GMm/r^2, or consequently a=GM/r^2. The acceleration (and thus, future position and velocity) of an inert object in space is independent of its mass. So all you need to tell where it will go is to know where it is, and what is it's current speed and direction of movement. And, of course, what other bodies influence it with their gravity.
Of course, in practice, there are other considerations in which the mass may become relevant. For instance, solar radiation acts on the surface, impacting force that's scaled by object's mass. The same is true for collisions with various stray atoms, especially prevalent near planets with atmospheres.
But discounting above factors (and, again, you can go pretty far just ignoring them), if you have two objects very close to each other and not moving relative to each other, they'll just go together along the same path for a long, long time.