I have just about given up on LED replacement bulbs so I have come up with another cunning plan!
According to the Bosch Automotive Handbook (7th ed) a 21W Brake bulb puts out 460 lumens and a 5W Tail light 50 lumens (surprisingly low I know) when new. My research into headlights tells us if we consider output at 13.2v to be "100%" rated output: when operating voltage drops to 12.54v bulbs produce only 83 percent of their rated light output. When voltage drops to 11.88v bulb output is only 67 percent of what it should be. And when voltage drops to 11.22v bulb output is a paltry 53 percent of rated output. So our 460 lumen stop bulb becomes 222 lumens when voltage at the socket drops to 11.22v. As the wiring for the brake lights has to run from battery > ignition sw > fuse panel > brake sw > connectors > back of car > bulb socket it is quite likely the voltage drop is considerable. An effective solution would be to fit a simple relay in the boot area with PVC 44/0.30 25Amp cable direct from the battery terminal (as I did with the headlight upgrade) to power the lights. A second relay could be added for sidelights as well. The relay's cost about ?4 each and the cable about a ?2.
85 - Green/Purple from brake sw
86 - Black (earth)
30 - 44/0.30 25Amp cable direct from the battery terminal
87 - Green/Purple to brake lights
For side lights (same type of relay):
85 - Red from light sw
86 - Black (earth)
30 - 44/0.30 25Amp cable direct from the battery terminal or tee'd to above relay terminal 30
87 - Red to side lights
If you are locating these relays in the boot area you should put 0.47 microfarad capacitors across contacts 30 & 87 as a spark suppressor and ensure the relay case is sealed with silicone or glue - there is always the smell of petrol in the boot of an E-Type!

Alternatively you could mount the relay in the engine compartment close to the hydraulic switch and just run the 44/0.30 25Amp cable to the brake lights.
This simple mod should almost double stop/tail output from the existing setup.
Note: LED's also dim with a reduction in voltage. If you want to use an LED bulb to replace a stop bulb you need one with at least 460 lumens to equal tungsten filament. If you want brighter than tungsten you need even more lumens and the LED's must be the same colour as the lens (red in this case). Current LED's are only about 40% efficient so if the manufacturer quotes 500 lumens you get 200 lumens. To prolong the life of high output LED's they need a heatsink.