Yes, a similarity with the original post!
At your light switch, as you suspect, the cable you have there is not a live and a neutral. They are both "live" wires, one (probably the brown) is permanent live supplied from your fusebox, and the other (probably blue) is the switched live that connects to the lightbulb. So to mimic the original light switch with the timer, the light switch brown would go to "L in" and light switch blue to "L out" of the timer.
But then you would still need a neutral to "N in"
It sounds as if the blue you have found in the junction box is actually a neutral, as the timer has come to life.
The next important point is that you need to be sure the junction box you have connected to is on the same house circuit as the light.
If it is, and you still have your new L and N feeding the timer, try connecting the switched live of the old light switch to "L out" of the timer. If you have a multimeter/volt pen gadget you should check the switched live to the bulb is the light switch blue wire, however your experimenting already seems to demonstrate that blue is switched live to the bulb.
If the neutral you've added isn't on that lighting circuit, and you have RCD's in your 'fusebox', you may have them tripping.
Alternatively you could do this:
Light switch brown to "L in" of the timer
Light switch blue to "L out" of the timer
Your new neutral to N in of the timer.
Your new L safely isolated.
You don't need to switch the neutral to the light, in fact you can't, as neutral is run directly to the bulb, so just ignore "N out" as not required.