When I drive my 1977 MG Midget, the headlamps dim, then brighten, then dim, then brighten…constantly. Dashboard lights appear to do the same. I have had no troubles starting the car since it was retrieved from storage in April. Any ideas about what might be causing this, aside from the ghost of Lucas? Thanks for your help! --KT
Does it dim at low rpm, brighten at high rpm?
No, it brightens/dims during highway driving regardless of the speed and also while idling, standing still with no rev.
Look at your ground cable between the engine block and the cars frame. Is the battery behind the seat or in the trunk? Sometimes long cables can do this.
The battery is in the engine compartment. I’m not familiar with a ground cable between the engine block and car’s frame.
There is a cable, 10 ga or larger, usually a flat weave type that goes between the engine block and the firewall or frame. Otherwise, there will be two ground cables from the negative terminal of the battery, one to the block and one to the body.
The purpose of this cable is to keep the engine and the body at the same reference ground. Without the cable, you get a condition on the engine called a floating ground. Your lights are grounded to the body, but the battery and alternator are grounded to the engine.
If one of the connections of this cable is not good and solid, and conductive, the engine ground will float to a different potential from the body. This will result in your headlights, and all other accessories to see a varying voltage.
In cars of this era, this cable is usually at the back of the engine to the firewall.
My TR6 does this sometimes as well. My solution is just not to drive it at night 
Check where the wires are grounded to for rust, it makes a terrible ground. Also, make sure that it’s a metal screw grounding to a metal body. One of the problems I had with my old Chevelle was someone used a plastic screw to ground one of my rear lights to the bumper and that made for a terrible ground.
Guys It is a MG Midget, that's the way they are designed. ☺The trouble could be due to a problem with the charging system. Check the voltage getting to the battery while the trouble is occuring. If the voltage shifts up and down with the lights then check the connections of the charging system to make sure they are clean and making good connection. The alternator or voltage regulator could have a intermittent internal problem also. Make sure the fan belt is tight.
If the charging system is ok then check the light switch to see if it has a problem. Make sure the input voltage to it is steady.
I attempted to get an education many years ago and to help support myself I repaired cars in a back yard shop. No one in the town worked on European cars and I was familiar with them so I stayed covered up. Electrical problems on British cars was by far the biggest problem and tarnish on connections was often the culprit. It became SOP to remove all the fuses and disconnect all harness connections and with strips of fine crocus cloth clean the contacts, lubricate them with Lubriplate and put everything back together.
In some respects, it is a good thing that they ‘don’t build them like they used to’.
Everyone knows a Lucas lighting system has three settings. Off, dim, and flicker.
Tester
That reminds me Tester. I was told that the Model T had three speeds, idling, clunkering and licketty split.
But I have owned several MGs and Austin Healeys and enjoyed them as toys. They were a lot of fun. When new the UK cars seemed quite reliable but they didn’t handle aging very well. The electrical system was the worst but those SU carbs could be a pain at times also. I would enjoy having that old A-H 3000 back today.
In cars of this era it is typically the voltage regulator causing overcharging.