Low voltage on circuit after breaker turned off - induced or backfed voltage?

Question

I was planning on installing a programmable timer on one of the 4 single-pole switches on a circuit. All of the 4 switches control various lights towards the front of the house, one of which is a pair (2 pairs actually) of motion-sensor lights.

After turning off the breaker for the circuit that controls these 4 switches, I used a non-contact voltage tester to make sure everything was cold, but to my surprise I found that the live wire still made my tester chirp and alert me of a low voltage presence (i.e.2 out of the 6 leds on the tester lit up). I then proceeded to switch off more circuits at the breaker, and eventually the tester stayed silent when I tested the live wire again.

I'm obviously a novice but have done a bit of reading up before posting here. I've read a bit about "induced voltages" that show up as a result of other live wires being in proximity to the wires in the circuit in question. I've also read about "backfed voltages" that are a result of equipment on the circuit (I know some motion sensor light have capictors in them..) or are the result of other circuits.

Since the low voltage disappears when I turn off some of the other circuits, I'm still left questioning what the culprit is...and if I need to be worried at all? The reason I'm worried, is because my timer requires a neutral. So, if the culprit is of the backfed variant (specifically from other circuits) I don't know if that impacts tying into a neutral (or does it not matter in any case)?

I'm not sure the image helps at all...but I figured people always like pictures. 
Am I overthinking this all, or can I just tie into the bundle of neutrals (circled) regardless of why there's low voltage on live (yellow highlight) with the circuit breaker off.

Thanks in advance - and please go easy on me if I've said (many) stupid things.

Max Power · Answer

It's hard to say without much more information about the circuits, but it is likely capacitive coupling between closely routed circuits. I've seen over 70 volts when testing a circuit that shared a conduit with a live circuit. Old meters didn't pick this up because they had relatively low internal impedance that allowed the voltage to drain quickly, my good digital has a very high impedance that does not shunt the voltage as fast as it builds up so I see the 70 volts(but is good for testing low amperage circuits). 
Capacitive coupling of this nature is very low total energy, kind of like a static charge it can't supply much current.

And be careful using cheapo meters on mains supplied circuits, they often have incorrect(12volt glass) fuses that will explode, arc, and burst into flames if you accidentally overload them or have the probes in the wrong holes.(eg. in the amp sockets when you think your testing volts, see https://youtu.be/R2ngaZwOgGM)
"Fluke T5-600" is great if you only do house wiring (simple single range so no good for fine electronics) won't break the bank, clever shape doesn't need 3 hands, and will last for decades.
I have a cheap $40 meter too but I only use it for current-limited devices.(small-battery power)

Low voltage on circuit after breaker turned off - induced or backfed voltage?

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