Well, there are 2 switches in the right orbit, so which one are we talking about? Here are some things to consider:

1. Any recent plunge from the shooter lane will cause both switches to get ignored for a bit.
2. Any recent bumper hit will cause the lower switch to get ignored.
3. Any recent Gandalf loop shot will cause both switches to get ignored.

If a ball is in the bumpers, a solid shot up the right orbit that makes the 2nd (high) switch should work just fine.

If you really are having strange problems with it not working, I would suggest something is shorting out one of the switches that causes ignores - any bumper, top lane, shooter lane, or gandalf (although I would think this might be obvious if lights are blinking, sounds happening, etc.). Further, if it only seems to be during ROTK, it could also possibly be something only shorts when there's a ball in the lockup (ROTK and FOTR will do their best to leave one ball in the sword if it's there, but you'd likely never notice an issue during FOTR since it's not used). So, check for shorts, then check for shorts with a ball in the sword lock would be my advice.

Absolutely not; I gave you some clues earlier. Bumper hits cause the low switch to get ignored because the game assumes it's draining from the bumpers. The high gate is never ignored WRT bumpers, so if you make a solid shot (or get a lucky dribble down from the saucer kickout), you will get awarded the orbit.

If there is no recent bumper hit, the low orbit switch will award the orbit, and the high one will get ignored.

There is a metric crapton of logic that goes into orbit switches that most people take for granted. Believe me, it's far more complex than what little I've described so far.