I wasn't trying to be evasive. I use Ilford Rapid Fix or Hypam (similar products; ammonium thiosulfate slightly acidic rapid fixers) at "print strength," i.e., 1+9, for both first and second fixing baths. I fix 1.5-2 minutes in each bath. I am familiar with the Ilford "archival sequence," but have reservations about using one fixing bath at 1+4 for one minute.
First, using that method and fixing to even Ilfords "optimum permanence" standards, the capacity of the fixer falls to 10 8x10-inch prints per liter; kind of wasteful in my estimation. Secondly, there is some doubt about whether the Ilford sequence is adequate for other papers, especially those that have more silver halides in the emulsion.
The idea of the Ilford sequence is to use a strong fixer so that fixation occurs completely before the fixer has had a chance to soak into the paper base itself. This latter happens at about 1.5-2 minutes. Keeping the fixing time short and not saturating the paper base is supposed to speed up washing. I don't mind fixing longer and washing appropriately longer, so I use a more traditional and more economical two-bath fixing regime. For me, one minute total in the fix seems just too short. Heck, I have a hard time keeping it to 2 minutes per bath...
Other fixing regimes and other fixers work just fine. Mine is tried and tested, and I trust it, so I stick with it.
One advantage of using the weaker dilution is that is seems to be neutral enough in pH to allow me to transfer prints directly from the second bath to the toning bath without any staining. If this were not the case, I'd likely use one of the alkaline fixers for the second bath.
Hope this answers your question.