My preferred method is to allow a cutting to callus, and then to plant it directly in the soil in its permanent location. I have never taken the additional step of first rooting the cutting in air or in a temporary medium like perlite and gravel.
The main reason to withhold water during the rooting process is that without roots to absorb moisture from the soil, the cutting will just sit in damp soil and risk developing rot. It has no way to absorb or benefit from the moisture in the soil until roots are there. Before striking roots, the moisture does not help the cutting, it just puts it at risk for rot.
After a few weeks or months, when roots start to form, you can see the change in the cutting. A cutting that was doing nothing for a month or two will all of the sudden start to errupt with new growth. Thats the sign that the roots have started, its drinking water again, and growth phase is on! And since the cutting is already planted in its long term location, there is no worry about damaging the baby roots by digging the cutting up and re-planting it.
Jagube I'm not sure about your cutting in perlite and gravel. I've never rooted in that medium before and so I'm not sure what to expect with it. All the best.
But I know that what I have described above works and is safe for cuttings. I have planted many cacti this way, with very few setbacks, and minimal etiolation. This is how these two cuttings will be planted once they callus. Its very important to minimize the risk of rot. Rot is the greatest killer of cuttings.