Firstly, there isn't a lot of demand in Thailand for some kind of substitute teacher who flits between different schools perhaps covering for absent teachers, etc. In truth, there never has been a demand for this sort of position.
Maybe one or two of the larger private language schools who supply teachers to Thai secondary schools might sometimes have a vacancy for a supply teacher, but you would still be classed as a 'full-time' teacher for that particular private language school (agent)
The thing is you still need a work permit to do this type of work so technically you need a non-immigrant B visa in order to start the work permit process.
Visas don't entitle you to work legally (there is no such thing as a 'work visa' in Thailand) To work legally, you still need a work permit. And it would be nigh on impossible to get a work permit as a substitute teacher working for several different employers.