In my (very limited) experience a mustache wax needs to be soft enough to apply, but firm enough to hold.
With a wax/fat/oil based formula which has a temperature based viscosity, doesn’t work very well. As body heat melts the wax after a while.
You also want to have a wax which you can removed at the end of the day.
My experiments with adding a resin and solvent were, well painfuly unsuccessful.
After reading this I decided to try out baking soda.
It works! I mixed roughly equal quantities of bees wax, coconut fat, and baking soda. And a very small amount of water.
This made a wax with a nice smooth consistently which was easy to apply and dries/hardens/does not melt. So far (8 hrs) has been holding well.
So I would say the baking soda acts as a filler which is also (water) soluble, so can dry and harden a little bit.
Downsides, it was a little bit gritty.
It needs some more experimentation, and I want to try with glycerin.
Overall a fun experiment ????