While all this is interesting, I think we risk confusing the issue (and the OP).
Plus, using really dilute fixer for extended times may be a viable practice, but it's hardly mainstream and may have some problems achieving complete fixation due to the consequences of the weaker dilution. I have experimented with this in the past and wouldn't feel confident recommending it to anyone. I'll stick with the tried-and-true best practices and the manufacturers' recommendations for the most part.
Fixing time has a direct correlation to dilution and type of fixer. Sodium thiosulfate (conventional) fixers take longer than ammonium thiosulfate (rapid) fixers. A higher dilution of either of these requires more time. Longest times would be with diluted conventional fixers. Shortest times with strong rapid fixers. For film, the clearing test will give you a reliable indication of what times you need as well as when the fixer should be discarded. With prints, we need to test and use throughput. It's really that simple.
Choice of fixer type, alkalinity and dilution are a matter of workflow.
@Umberto (and others who might be interested),
It was pointed out to me recently that the Ilford sequence for optimum permanence without toning only calls for a final wash time (after the 10 minutes in the wash aid) of five minutes. The final wash time with toning is 30 minutes. The difference (as was also pointed out to me) was that selenium toner contains ammonium thiosulfate, which soaks into the paper fibers during the toning time. The short wash without toning is based on the short fixing time, which prevents the ammonium thiosulfate and other fixing compounds to soak into the paper base.
The logical conclusion of this is that adding selenium toning to the mix effectively negates the advantage (i.e., the short wash time) that is gained by using strong fixer for a short time. With the toner, one has to wash just as long as with other fixing regimes (e.g., weaker rapid fix for longer times or conventional fixers, which require 5-10 minutes in the fix).
Therefore, there is no reason to use short fixing times with strong rapid fixer if the prints are to be selenium toned other than that the user prefers this. In my opinion, however, the short fixing time is awkward and difficult to achieve in practice, especially with larger prints. Furthermore, the short time almost excludes the two-bath fixing regime for all but the smallest of prints; just try making sure a 16x20-inch print gets exactly 30 seconds each in two baths and has enough time to drain before it hits the water rinse tray on the 60-second mark. Add to this that the one-bath capacity for strong fix at this short time is only about 10 8x10s per liter (which I find wasteful), not to mention what happens when any refixing needs to be done (e.g., after bleaching) and you see why I've opted for the weaker "print-strength" solution of rapid fixer and two-bath fixation.
I primarily use Ilford Rapid Fixer or Hypam, but have used other ammonium thiosulfate based rapid fixers (Kodak, Tetenal, alkaline fixers too) as well in the past. They all work in a similar manner. Ilford lists the 1+9 dilution of their fixers for manual processing of prints. The fixing time is given as two minutes for this dilution. However, this should be viewed as a minimum. Since the paper fibers are going to get saturated with fixer at this time and wash times will need to be appropriately extended, adding a few more seconds doesn't hurt at all; print degradation from fixing too long doesn't start to appear until about 8-10 minutes of total fixing in ammonium thiosulfate fixers.
So, I use "print-strength" fix for 1.5 minutes each in two fixing baths; a total of three minutes. A good 30-40 seconds of this extra minute, however, is drain time. I make sure the print stays immersed and gets agitated for the full 60 seconds (or a bit more) in each bath, then I pick the print up by a corner and let it drain. This can easily take 15-20 seconds, especially for larger prints. I tone, treat in a wash aid and wash for minimum 60 minutes. I test for both residual silver and hypo regularly, so I know this works.
As for testing: for those of us who selenium tone, there's no reason to mix up ST-1. The residual silver test with selenium toner works just as well. Mix a small amount of selenium toner 1+9 (Kodak's recommendation) or stronger (I use 1+4 since I have it on hand; results are the same). Apply a drop of this to the print border or other completely fixed-out areas of a test print and wait 2-3 minutes. Any tint other than a slight (almost unnoticeable) yellow tinge means that the prints are not adequately fixed. These prints should be refixed and your fixing regime adjusted accordingly.
Sorry this got so long, but I hope it helps,
Doremus