First of all the "R" wire has nothing to do with the ability to crank.
The S wire is the "trigger wire" that fires the solenoid. Doc, is 100% correct as usual but let me put it in other words.
The OEM starter is HOT all the time. This is the large battery cable in the center. The "s" terminal is just a solenoid wire that engages the starter. The "R" wire is a "hot shot" wire that provides a FULL 12 volts back to the coil during cranking and in reality bypasses the voltage drop resistor that powers the coil in the normal run position.
So if you are lacking power to that wire during cranking and you are POSITIVE that its the correct wire that should be on the S terminal, you need to backtrack the wire and find out where it is losing power. It goes back to the ignition switch via a Neutral safety (in the case of an automatic trans).
This wire should have a full 12 volts and your test light should be as bright as if it was connected direct to the battery.