I wonder -- if the push vehicle per se must be radio- and fire extinguisher-equipped. Most of the time the push and the support vehicle are one in the same -- but something such as a quad-wheeler that stays at the start line (or returns to the pit but doesn't go fetch the race vehicle) might be allowed to NOT have the radio and f/e. Check with SCTA and let us know, hey?
That said -- both of those devices are relatively inexpensive and darned handy to have available no matter what vehicle they're in. We've got fire extinguisher and CB in the support truck - and fire extinguisher in the pit trailer -- and planning to add a CB there this winter, too. And a first aid kit in the truck -- well-labeled and always easy to find (not buried under rubble or the plastic sheeting). Putting First Aid in the trailer, too.
Safe is cheap.