This is a typical installation of the dual stage air-assist in the Nova series machines. Your configuration may differ slightly.
The maximum recommended operating system pressure, according to Thunder China Engineering, is now 40 psi to help prevent premature air solenoid failures.
This is the back side of the main air inlet on the rear of the laser. Line #1 is supplied from the compressor at the inlet and travels to the solenoid bank.
At the solenoid bank, #1 splits and goes into the inlets of the 2 identical air solenoids (these are normally closed valves).
Then lines #2 and #3 go to their respective needle valves. the 2 stages exit the valves and combine back into one line, line #4.
#4 runs to the nozzle
The TL Timer board controls these functions: Nova Series DSP TL Timer V8 Block Diagram
The dual-stage air-assist retrofit installation guide contains all the parts, wiring diagrams, etc... of the dual stage air system: Retrofitting Dual Air Assist (thunderlaser.com)
Here is more on air: https://support.thunderlaserusa.com/portal/en/kb/thunderlaser-usa/manuals-documentation/air-assist
Here is a video overview and a note about using 2 different air sources (stock pump for low stage and an external compressor for high stage: