From how I see the pictures you have the SSR wired to the thermocouple terminals, not sure why you are wired to ALM1, and not really clear on where power is coming in.
Power should come in on pins 1 & 2
SSR pins 4 & 5
pins 9 & 10 if you have a K type thermocouple.
The schematic is on a side of the PID, what we are missing is a close photograph of all of the screw terminals on the back. It appears the PID is actually upside down in the bottom photo as compared to the schematic which can be a little confusing.
If that is a FOTEK SSR, check your red and blue wire polarity at the SSR. I think you have them reversed. Should not hurt the SSR, but it will not work if I'm correct. You want POSITIVE to POSITIVE and NEGATIVE to NEGATIVE. Also see below for other common pitfalls of SSR to PID and temp sensor wiring.
1) Do you have power at the PID - is the display turning on.
2) Did you step through the internal configuration of the PID to see what the default settings are set to (I know you talked about buying a Auber PID, but the one you messaged me about was a 1/8 DIN package so this is clearly not that PID as it is a a 1/16 DIN package. If you bought it of eBay, a lot of those are pre-used and the settings internally can be pretty much anything. Use the manual and step through and verify all of them, especially the output type and temp probe type. It needs to be set to an SSR control voltage output. I have also seen people get bad SSR's from eBay and China before. Also there are some PID's that just don't have SSR output at all. It depends on what you bought (post a photo of the model number sticker with the rest of the details).
3) Is the light on the SSR coming on at any point? It's not impossible to have a bad SSR (again if from eBay the odds go up greatly). If the red LED is coming on, it should be closing the load side of the SSR to power the light.
4) If you wired the bulb straight (bypassing the SSR), does it light?
5) A meter would expedite all of this testing.
6) also if room temp is say 75* and you set the PID to to 100*, the process light on the face of the PID should also come on (does not need anything other than the PID and temp sensor for this to work). If you are not getting a process light you have an issue in the PID or PID configuration. Also double check your probe type vs the probe type configuration as if it's set for a K and you have a J type sensor, it's not going to read right. I presume it's not a RTD type as they normally have 3 wires and your photo shows 2.
If it's not the SSR polarity, my money is on either a bad out of the box unit (could be either PID or SSR), or the PID internal setup is not configured correctly for the rest of the setup.