Separate circuit, but why is the disposal causing lights to flicker?
If the light does flicker also if a hairdryer or vacuum cleaner
is connected to the same outlet/box as the garbage disposal, it is
likely a problem upstream the location where both circuits (light,
garbage disposal) are connected.
      A loose connection acts as voltage divider in combination with the garbage disposal or any other big load.  F.e. backstab
connections are known for problems.
If the light does not flicker if the garbage disposal is
replaced by a hair dryer or vacuum, it could mean that the garbage
disposal motor emits some energy, e.g. HF or inductive surges, that
disturb other electronic devices nearby. Maybe the motor capacitor
has gone bad or the graphite elements/sliding contacts are worn out.


In both cases the motor should have less power compared to an installation without any problem.