When I press the brake pedal the lights (dash light, brake light) dim out. Added to this when I accelerate, lights also dim at times and the car seems to stumble lightly as though its missing spark.

I'm under the assumption that one of the grounding points on the car is loose.
I've checked the one on the firewall which connects to the back of the UIM.
Apart from this where else could I check?

Setup is a stock Series 7.

 

There is another ground on the left side of the engine near the plugs. Another on the exhaust down-stream of the O2 sensor at the connection between the cat and cat-back flange bolts.
You can check & clean those but most also add grounds. Simple and cheap:
(1) Neg battery to engine
(2) Neg battery to Chassis
(3) Chassis to engine

 

Problem Solved. Although lights still dim out very slightly the 3k hesitation is gone.

I made extra grounding from Neg battery to chassis, chassis to alternator, and UIM to under the intake filters.

I'm not too sure as to the exact location of the Engine Block A, i.e under the UIM near the vaccumm chamber. Anyone have a clearer picture than those provided by the Damian Hyper Grounding Post?