There needs to be more information on the PID controller. If pins 3 and 4 are just connected together when the output is ON then there is no power to the SSR.
You need the input parameters.
Original wiring diagram in post#1 for PID. What other info would you like to know? My apologies, I know next to nothing re electronics.
Input parameters??? I have set the PID to use K thermo, to heat, set to use SSR. Is this what you mean?
If the wiring is wrong, can you point out what needs to change, using the original wiring diagram in post #1 as a reference?