But what I was more interested in was how and where the resistance would be applied in, particularly, a scenario like a paired partner kata with bokken. I'm just having a really hard time wrapping my mind around how that resistance could be manifested in such an exercise. Which part of the resistor's sword would be applying resistance to which part of the resistee's sword?
It depends on the movement, and the resistance is not necessarily sword-on-sword. It could be (and often is) sword-on-body. For example, in the basic movements I do in paired bokken training (technically they are not kata but dosa, although they are practiced the same way) the attacker repeats the same attack on both sides, advancing a step each time. The defender remains stationary until forced to move by the attack, at which point he steps back and receives the attack with his sword. If the attacker does not perform the attack correctly enough to force the defender to move, the defender will "resist" by holding his ground and turning his sword into the attacker to cut him as he advances. Whether the defender "resists" in this way depends on how the attacker's movement feels and whether it is being done properly enough that the defender feels like he is in imminent danger of being cut and must move to avoid that. I think it is something that I would have to show you in person for you to understand the subtleties of when to move versus not move in this kind of practice.