ESP8266 noisy input when wires go through power supply
Noise is coupling onto the line, with enough current to create a voltage drop across your pulldown resistor.
The quickest fix would be to use a stronger (lower R) pulldown resistor.  R=1k would be much less likely to false trigger, and would only draw 11mW.
The next step would be to filter the noise, using a ferrite on the cable or adding an RC (watch the time constant) filter near the input.

This circuit has the following properties:

No voltage divider: input will (eventually) reach full 3.3V
C1 charges through R2: rises to 2.1V (63% of 3.3V) in 1 millisec (R2*C1)
C1 discharges through R1+R2: drops 63% (3.3V to 1.2V) in 2 millisec ((R1+R2)*C1)