Cactus Cuttings Not Rooting -- Please Advise

About a month ago, I started a thread on my cactus that had become partially rotten (see http://forum.auscactiforum.net/t1329-cactus-needs-urgent-help-please-advise). The cactus had a Hylocereus base (which was rotten) with several Mamms grafted on top. Luckily the top part was not rotten.

I cut the Hylocereus base completely off and also removed several small Mamms from the top. So now, I have several small Mamms and one large part of the former top. The Mamms and top have been drying on a shelf for the past three weeks and the cut surfaces are now calloused over. They have not been sitting in soil.

Neither the Mamms nor the top show any signs of rooting. I am a cactus novice and am concerned that there are no signs of rooting even after three weeks. Should it take this long for the roots to start to show?

Is there anything I should do at this point before putting the cuttings in soil?

If it is time to put the cuttings in soil, how moist should the soil be and how often should I water the cuttings?

Any advice would be great!

https://i.servimg.com/u/f46/17/16/83/60/cactus13.jpg
https://i.servimg.com/u/f46/17/16/83/60/cactus14.jpg

hi kaktus! dont rush with rooting! in our cold, european climate rooting takes time.. sometimes 2 months, someimes more (depending on species), and the best period for rooting is summer. better leave it cold and dry antil may and then start watering your soil accurately.

Thanks for the advice, Numan. I'll let the cuttings sit and just wait for the roots to show.

I cut cactus in autumn and keep them on empty black plastic pots.
You can keep a dark condition on the cutting face in this setting.
Aerial roots will come out from the cutting face in spring.

Thanks Hanazono