Material to prototype gear designs
Balsa wood is available from many sources and can often be found at local outlets. Various thickness panels are usually presented in shelf units or organizer caddies, typically in 24" or 36" lengths (0.6/0.9m) and varying widths.

Balsa wood is quite soft and easily cut, more easily than foam core as it is consistent throughout the thickness. There will be weakness parallel to the grain, however, which means gear teeth will break off if too much force is applied.

One could create the model components and then apply a thin layer of PVA glue along with a paper reinforcement layer to mitigate the grain-parallel weakness.

1/8" balsa (3mm) can be cut with a sharp razor knife, but I believe you'll have better strength with 3/16" to 1/4" material (4.75 to 6.35mm), especially if you apply paper reinforcement. If one layer on one side appears insufficient, apply a second layer on the other side. It would then be the equivalent of foam core board with a much stronger inner ply.

Balsa sands to a very smooth surface. You could then apply a thin layer of glue if you require a harder contact area for reduced friction.