See schematic below. Note that my design makes the following assumptions:
1. Use of PID in ON/OFF mode (or long duty cycle), PID does not pulse width modulate the SSR.
This setup allows me to use the voltage resistance SSR (phase angle control) to adjust the power/intensity in manual or auto mode and use the PID relay output to enable/disable the AC contactor and heating element based on temperature. In my test run I ran the recirculation and hit the strike temp within 1 deg F. Form what I understande, the EBCIII PID is configured the same way. During the mash I will also be able to use the minimum power setting (about 2000Watts) to prevent scorching of the grains.
2. Use of a low power 15W pump, <1amp at 120V AC.
This allows me to use the wiring scheme shown below which includes the PIDs internal relay (3A max) for the pump "Auto" feature, the pump is on when the element is on. External relays and different wiring are required for a higher power, higher current pump like the March or Chugger pump.
Also note that the PID wiring is for the MyPin TA4, the popular Auberins PIDs have a different pin out.