Any idea why a random lamp or lamps would pulse when another series of lights are turned On? The lights in our building is on a multi branch circuit, I'm guessing it has something to do with the shared neutral.
Whatever the problem is it's not because the lights are on a multiwire branch circuit. Stop focusing on some superstitious fear that isn't based in reality.
The whole North American Continent is fed with power that shares a neutral. There may be some bad wiring causing problems, but electrons are too dumb to know what circuit conductor they are traveling around on, and LED lamps don't care what kind of circuit they wired to.
I think it's far more likely that cheap LED lamps are the problem.
You clearly have a single shot transient problem that only occurs at some turn on time. To light an LED for a moment it takes some amount of energy.
You have lights that are turned on and off by some sort of switch. What is the actual switching device between power (the hot wire) and the actual lights that flash when some other circuit is turned on? Is it an ordinary mechanical wall switch, mechanical contacts on a relay, or some sort of electronic switch?
How long are wire runs where hot and neutral wires are close together? A 4 ft long LED bulb will take a moderate amount of energy for a momentary flash. Could a 1000 pfd (0.001 ufd) capacitor provide enough energy?
An LED driver probably has a fairly large input capacitor with little current limiting in series. After being off this capacitor has near zero stored charge. If turn on to this capacitor occurs at an AC voltage peak, then you can expect a large input current spike at this turn on.
How could such a large current spike couple to what you think is an unconnected LED? Also there are likely large voltage spikes.
(1) How many different LED fixtures in one room?
(2) How many different switched LED circuits in one room?
(3) How many switches in one box?
(4) How many different switching locations are in one room?
(5) How big is the room?
(6) Are all the lights in one room on the same phase?
(7) Are all the LEDs controlled by one switch close together in the room or scattered amongst LEDs on other switches?
(8) If you toggle on and off one circuit of LEDs what percentage of time does an LED flash in another circuit? Is it always in the same other circuit?
What does a tombstone have to do with the problem? I think that you can consider a single fixture when disconnected from its supply wires at the fixture to have almost zero likelihood of flashing from adjacent wires.
To get electrical energy to a load you need some sort of closed electrical circuit (excluding radiated radio frequency energy, I think we are only concerned with conductive, capacitive, and inductive components describing your circuit).
Assuming your switches are really open when off, then to get energy to the flickered fixture means there has to be some form of capacitive or inductive coupling to the flickered circuit.
A very remote possibility is a very large transient voltage at the switch box that causes electrical breakdown of the open switch. I view this as a zero likelihood.
I don't believe there is inductive coupling.
Very likely you have capacitive coupling. You might have 20 pfd per foot between some wires. At most it is unlikely you have more than 60 ft of two hot wires from different circuits this closely coupled. Suppose you did, then the capacitance is 1200 pfd. Can I cause a flicker in a fixture with this amount of coupling? Depends. With sufficient voltage it might be possible.
I don't know your voltage. But get a 0.1 ufd capacitor or somewhat larger of sufficient voltage rating for your circuit voltage. Connect this capacitor between neutral and the hot wire to the fixtures that flicker on the output side of the switch that is off. The connection might be made at the switch box or anywhere near a fixture. See if this eliminates or in any way changes the flicker. This creates a capacitive voltage divider that should greatly reduce the source of voltage to a fixture, if capacitive coupling is the problem.
If capacitive coupling is yor problem, then you need to change the way wiring is run.
Thanks, the flicker happens in the circuit that is already on, when the other is turned on.190426-2032 EDT
With inductance in a circuit and current flowing the opening of the circuit can easily produce thousands of volts to initiate a spark or arc across the opening element. This how an old automotive ignition coil works.
To test the sensitivity of electronic circuits to transient noise I have simply rapidly oscillated a plug to a two bulb 8 ft Slimline fixture.
Will arcing of a set of switch contacts in some fashion couple enough energy into a turned off LED circuit to momentarily flicker the LED? I don't know. But you may have demonstrated that it does.
At this point you need to define some words and run some independent experiments.
Flicker could means a number of different things. Is it a single shot event? Does it means 120 Hz ripple on light intensity? Not in your case, but it did in Russs57's comment. Does it mean an increase in intensity, or a decrease? Is it a short duration oscillation in intensity? Or etc.
Consider two 120 V switched 100 W bulbs fed from the same phase and sharing a common neutral of 10 ohms. A cold 100 W 120 V incandescent bulb is about 10 ohms, and hot about 144 ohms. With one bulb on its voltage is about 120*144/154 = 112 V. You would see a brightness difference in the bulb compared to a circuit with a much lower neutral resistance.
I have selected the bulb size and neutral resistance such that you can easily experiment. 100 W incandescent bulbs are still around, and a moderately stable resistance at 1 or 2 A and somewhat near 10 ohms is the resistance of a 1500 W space heater.
At the instant the second bulb turns on the voltage across the two bulbs is about 120*10/10 = 60 V. Actually a little less because you have 144 ohms shunting 10 ohms, or 9.35 ohms. So you will see a short time flicker in the dimming direction of the initially on bulb.
Now suppose the two bulbs are supplied from opposite phases. The 10 ohm neutral initially has a voltage drop of 120*10/154 = 7.8 V with one bulb on. At the instant that the second bulb is turned on two opposing currents exist in the neutral. Doing the math just after the second bulb is turned on I get a voltage drop across the 10 ohm resistor of about 54 V. This is in a direction to add voltage to the initially on bulb so that the already on bulb sees about 120 + 54 = 174 V. Thus, the already on bulb brightness momentarily increases a lot, bright flash.
When the turning on bulb reaches its high resistance the 10 ohm resistance has a voltage drop of about 0 volts, canceling currents thru the neutral, and the initially on bulb is slightly brighter than when it was the only load. You may not detect this.
The above is a suggested experiment that I have not played with but may illustrate how neutral impedance can affect components in a circuit.
LEDs have ballasts (power supplies) that may be pretty much like an uncharged capacitor at their input before turn on. Connecting an electronically ballasted LED at a voltage peak and large peak currents may flow.