1995 Lexus LS 400 Stereo Cuts Out When Brake Applied

After the car has warmed up, this often happens while driving the car:

While in motion, the brake pedal is applied;

resulting in this:

a) the sound system cuts out and comes back on normally about 2 seconds later, even if the brake pedal is still in use;

b) both headlights flicker momentarily;

c) the cruise control disengages and shuts itself off;

Note:

Switching the headlights from Low beam to High beam will also cause the same 3 results (a, b & c) as listed above. The brake pedal does not have to be pressed down at the time the Hi - Lo beams are employed.

Perhaps you are able to suggest a fix for my problem?