Your last paragraph is telling… perhaps an example of projecting the ‘known’ past into the present, or a projected future… using the word ‘absence’ in your familiar way. The space between thoughts that Rinpoche is talking about is ‘open’, absent of your thoughts and continual conceptualizing. At least for an instant. That subtle ‘opening’ we seem to most often skim-over as being uninteresting, as we pursue ‘meaningful things’, when it is actually ‘essentially‘ interesting, and what Rinpoche is pointing to. So I think you are correct when you say, your usual use of the word ‘absence’ is, “not the sourceless source of present experience”.
However, in the first post of this thread above, the second quote begins with… “We should be able to go beyond the zero-point of origination to a knowledge that is zeroless… At the same time, going beyond must stay within ordinary appearance”.
Rinpoche seems to be saying we can still get a sense of the zeroless, that prior to the zero-point, without leaving ordinary appearance. Maybe we could think of it as the feel of the not-known [like wonder], or the sense of open possibility at the edge of the future. In the book, ‘Gesture of Great Love’, Rinpoche invites us to practice Ex. 11 – Newness and Nowness. p. 35 Such a gentle and calm practice. He says, “You do not need special experiences, fierce discipline, or formal sitting.” I think of the practice as a kind and gentle Edge of the Future practice, such as the one he describes in ‘Dynamics of Time and Space‘, p 99. You might say, at that edge less-edge, where the unlimited and indefinite future ‘kisses’ Being, is a sense of the zeroless.