OK, I'm getting warmer in my quest for seedlings from tomato cuttings.

I took a 15 gallon aquarium with a plexiglass top, and put my cuttings
in that. 78-80F, and about 100% humidity (unlike the 30-40% humidity
in the rest of the house). Spray water on the cuttings about once a
day. The inside walls of the aquarium are continually fogged.

Most of the cuttings in planting mix died (though these were all ones
that were planted pre-aquarium). A few are still looking good, ten
days later. That planting mix was not, I admit, sterile.

Stuck a bunch on cuttings six-inches deep in a bottle of sterile
water. Put those in the aquarium with the others. Those are still
looking good, a week later, but I sure don't see any roots. How long
should it take to get roots out of those tomato cuttings in water?

Geez, I didn't use distilled water. Should I have done that?

Grasping for roots here ...