Sorry misunderstanding - the tyres and rims just had to dip underwater so that the surface is completely wet - no need to squeeze the foam tyres so they soak up the water

It takes around just a few seconds to get the surfaces wet and also if you fix the foam tyre to the rim with the screwdriver under water there is just a little amount of water between the rim and the foam tyre (just enough to pull the foam tyre from the rim with your hands if you want to do this if the position of the tyre on the rim isn`t correct)...I just leave the tyres in a dry warm area overnight and they feel completely dry - if a good double sided tape is used you couldn`t barely lift the edge of the foam tyres from the rims...I will make a picture the next few days...
Tamiya: yes - they pack a few stripes of double sided tape in the old F102 kits (has a williams back in time) but as I remember not enough material to cover the complete surface of the rims and fixing the tyre on the rim was quite tricky - you had to lift off an edge of the cover of the ds tape, position the tyres on the rims and check they are sitting perfect enough and also the small white cover of the ds tape was on the outside of the wheel so you could remove it carefully mm for mm round and round - perfect if you manage not to tear the cover film and as the tyre sit perfect on the rim...in this case you don`t have to wait overnight to use your fresh tyres but also nearly no second chance to change the position of the tyres on the rims...
Aceton: Kimbrough offers a cone for Pro10 (and 1:12 also?) for this kind of foam tyre mounting... you put the glue (pattex) on the outer surface of the rim and on the inner surface of the tyre - let the glue dry for 10-15 (?) minutes - use gloves and an ol brush to paint the aceton to the glued surfaces (had to hurry up) - put the cone on the rim and push the foam tyre over the cone on the rim - fix the rim with the cone to the ground and turn the tyres with the second hand 1-2 turns around on the rim to get a perfect fit...what a mess

I use Pattex also to mount my 1:12 and pro 10 wheels also but I fix the tyre on the rims before, than push a screw driver between tyre and rim, push the srew driver a few angles sidewards so the foam tyre lift of the rim, let run a few drops of pattex in to the gap, tirn the wheel/screwdriver 1/8 of a full turn to the next position - than same thing again...also quite a mess...you need 2 hands and one leg...and cloves, old news papers, paper towels, brake cleaner...I will try to make pictures the next time I do this...
Today I think actual the 1.12 racers just use superglue to mount the foam on the rims...