Why can't I switch an SSR with another SSR?
The real problem is that you have chosen the wrong opto-isolator. The 2964270 is a pull-up device. You needed something more like the 2966595 in a 5 V input version so that you could pull A2 on the customer's device down to 0 V. You seem to have realised this and added R1 but set it way too high.

The OPT-24DC/ 24DC/ 2 (used in the customer device) states that to get a logic 1 you need > 16 V across its input. It also states that typical current at 24 V will be 7 mA. (It will probably be only about 4 or 5 mA at 16 V.) To get it to turn on your R1 value needs to pull A2 to less than 8 V. A 560 Ω resistor will pass 14 mA at 8 V so it would suffice. Bear in mind that when your opto turns on that Q2 will connect that resistor to +24 V and the current through it will be 42 mA with power dissipation of > 1 W.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A more complete schematic.