There are only a few spots on the board that are in play with
both the engaged
and bypass switch positions. That would be the input and output jacks themselves, the wires from the jacks to IN and OUT on the PCB, and the jumper wire from lug 8 to the eyelet marked 8. So you could start by reflowing the solder on all those spots and see where that leaves you.
That being said,
all of your switch wiring looks dicey to me, especially the jumper from 4 to 9, which is crucial for bypass signal. It is possible that this is the reason for the lack of bypass signal, and another unrelated problem in the build is preventing your engaged signal. If it were me, I would focus on getting bypass to work first. You could reflow the solder on lugs 4 and 9 of the switch, making sure there are no places where solder or wire strands connect to anything else. Be careful not to apply too much heat to the switch, because you can damage the internals pretty easily if you do that.
If you are the kind of person who works better when you know
why you're doing what you're doing, you can read about mechanical bypass switching in detail in
this excellent thread by Stephen.