What accumulates is mostly dried ink in the feed's channels, plus whatever the ink left behind as water evaporated. That is why the answer depends on the ink rather than on the calendar, and why every schedule you have read is right for somebody.
The early signs, in the order they usually appear:
- Slower start after a rest. Yours is doing this. A pen that used to write instantly after two days and now needs a moment is telling you the feed is not holding as much as it did.
- Reduced flow. The line gets drier and thinner at the same nib and paper. Your other pen.
- Colour contamination. New ink comes out slightly wrong for the first page.
- Hard starts every time, then skipping mid-word. By here it is a real problem rather than a signal.
You are at stage one and two, which is exactly the right moment.
A workable rule rather than a schedule you will not keep: flush whenever you change ink, and additionally if a pen has sat unused for a few weeks with ink in it. For a pen used constantly with one well-behaved ink, that can genuinely be a few times a year.
The method is dull: flush with cool water until it runs clear, then keep going a bit longer than you think, then let it dry properly nib-down on a cloth. Cool, not hot — heat is what damages the plastic parts and any adhesive holding the nib.