Click on the link below to the 6-minute video and verify that your wiring is the same as what they show. I have an Auber SYL-
2352 (close to your model) connected to an SSR in an older Bradley Original smoker and it works fine.
Auber SYL-2362 PID temperature controllerThe instruction manual for the 2362 says that it comes pre-configured for use with a K-type TC. If yours is something different it needs to be changed in the settings. Also, it's possible that it was accidentally changed when you were changing some other parameter. Double check that it is correct.
Also, I just checked mine and the OUT light only comes on and remains on while a signal is being sent to the SSR to supply power to the heating element. Be sure everything is wired according to Figure 2 in the instruction manual.
PID Controller terminals:
#1 (incoming power + or -)
#2 (incoming power + or -)
#6 (SSR +)
#7 (SSR -)
#9 (TC +)
#10 (TC -)
SSR terminals:
#1 (outgoing 120V power to heating element)
#2 (incoming 120V power - not from the PID controller)
#3 (from terminal #6 of the PID controller)
#4 (from terminal #7 of the PID controller)