I would be checking your settings...
My PIDs can run a few different ways, including running PID control via their own internal relays (low power, not suitable for brewing purposes generally) - I thik maybe you have your PID set to control via its internal relays rather than by outputting a voltage to the SSR.
If you can "hear the PID click on" then what I think is happening is that the internal relays are clicking on, and you have it set up to control a circuit that runs through them. A control voltage for a PID isn't going to be making any sound.
Read your instructions carefully and look at the output settings. You may have the wrong type of PID, but then again you may just have the wrong option selected on a perfectly good one.
Here are some snips from my PIDs instruction manual
outy
Method of controlled output
0,1,2
Note 1
Note 1 (applies to “outy”) :
0: Relay J1 as alarm output; SSR Disabled, normally used for upper or lower limit alarm trigger control
1: Relay J1 PID controlled output: SSR Disabled. Contact controlled output
2: Relay J1 as alarm output; SSR PID controlled 10 Volts DC output. No Contact controlled output
So of the three settings, 0 and 1 will run control, either as a simple setpoint alarm control or as PID through the internal relays - while option 3 is what you need to choose to run an SSR.
No idea whether even the idea let alone the actual instructions are applicable to your particular PID... but its probably worth a look if you hadn't been through all this stuff before.
TB
edit - posts since I started typing... Obviously your PID is different to mine. As a side note, I drive my RIMS by using the relays in my PID - I run something similar to Kevs diagram where I have an external 10A relay (contact) with a 12V control coil. A separate 12V power supply is routed through the PID's low current relays, the PID turns the 12V on and off, which activates the coil on the high current relay. I have a minimum control period of 2 seconds.... and it all works just fine. So even if your unit cant for some reason drive an SSR... a cheap mechanical relay and 12V power source will save the day.
Note - Kevs diagram has given me some ideas for my system.... thansk Kev.