The very first thing I'd do is reflow your ground connection on your in jack it looks ball like and could be dry inside if you want to check your grounds go to the end of this novel
I'm not familiar with how Aion wire their 3PDT switches it's not the way I wire mine
Anyway this is from their micro 3PDT bypass doc so I'd assume this is how all their standard 3PDT boards are wired
2,5 and 8 are the common row which either connects to effects mode (purple lines) where lug 1 input jack would connect to lug 2 pcb in carrying your guitar signal into the effects circuit, lug 5 ground connects to 4 (SW) grounding your LED and switching it on and lug 7 pcb out connects to lug 8 output jack carrying your effected signal to your amp
When clicked or stomped the other way the common row 2,5 and 8 would connect to bypass mode (red lines)
2 pcb in connects to 3 nothing, 5 ground connects to 6 nothing breaking the LED ground connection and switching it off and 9 coming from the input jack connects straight to 8 output jack bypassing the circuit
If all your connections are correct and have good continuity you should get bypassed guitar signal even if your circuit has a fault because it simply connects your input jack straight to your output jack as I say bypassing the circuit and carrying your unaffected clean signal out to your amp
So as PJS says you want to check you have good connections
if you have a meter switch it to continuity mode this symbol below, place your black probe in the COM port and your red probe in the ohms resistance port
I'd check your switch first check to see if your meter beeps from the common row lugs 2,5,8 to the top row lugs 1,4,7 (purple lines) switch it the other way and 2,5,8 should have continuity with 3,6,9 (red lines) then it's a case of checking your other connections have continuity
In bypass mode simply put one probe directly to the in jack tip and the other to the out jack tip, where your yellow and blue wires connect to the jacks
All your connections are labelled so it's easy to check for example your IN on the main pcb has continuity with your PCB in on the 3PDT board and so on, try to put your probes on the solder pads on your 3PDT board rather than the wire ends
A quick way to check all your grounds are good whilst it's in it's enclosure is, in continuity mode stick the black probe in a screw hole and touch all your ground points with the red probe like this, may not work with your painted enclosure if there's paint in the screw holes
In all the above if you get a beep it's got good continuity and therefore has an electrical connection