Okay, say a traveller accelerates away from Earth at 1g. Then he should never receive any light that lies further than one light-year behind him, right? This would be the Rindler horizon. Now after quite some time, another traveller accelerates away from Earth in the same direction at 10g, from behind the first's horizon. The relative proper acceleration between the first and the second would be 9g, correct? The relevant acceleration between them might be less than that, however, but certainly not zero or negative. So there should be some positive acceleration between the first and the second, and so the second should eventually catch up to the first within finite time.
But let's say the second emitted a pulse of light when he left, and according to relativity, no matter how fast he travels, he will never catch up to the light. So that light is forever in front of him. That means, then, that if he were to eventually catch up to the first traveller, the light will have already passed the first and now be somewhere in front of both of them. But the first traveller can never have observed the light in finite time because it originated from behind his horizon. That means the second traveller can never catch up to the first, regardless of his acceleration. But the relevant acceleration should always be positive, right?
I suddenly remember something publius was saying in the Interstellar Traveller thread about a negative acceleration behind the horizon, but I think I thought that was for the apparent acceleration for a pulse of light or something. I'll look back through it. I suppose it must follow for another accelerating traveller that originates from behind the horizon as well, regardless of the original acceleration, right?