The socket that plugs into the lifgt was burned up so i replaced it and now the light is not as bright as the right side i checked the grounds and even ran a ground off the battery to the light

Actually the bad ground is usually in the socket that you put the bulb in. The replacement socket is available at almost any parts store and are not hard to change just access the rear of the lamp and turn the socket counterclockwise then cut and match wires. This is almost guaranteed to repair this problem. I hope this helps. Take care.

IF THAT IS A DUAL ELEMENT BULB... That is a bad GROUND... DIRTY or CORRODED.

I removed my wife's left rear (BMW) found ugly spot and cleaned it with white vinegar Q-tipped the bulbs (very sparingly)... Applied CRC White Lithium grease... (again very sparingly)... From eBay pictures... I have been able to look at the (trunk-side) light... and I see no ground point in YOUR plastic housing... which means your ground issue is either right at your socket... or up the wiring harness. You can prove there is BATTERY there by simply putting a meter on the bulbs... and measuring voltage
to a GOOD GROUND elsewhere on the car (while the brake is being applied).

I am supposing that both elements will be powered... just missing ENOUGH GROUND to glow brightly (visibly).

Q-tipped the sockets... everything is peachy.

If it is a twist out socket... check right there with a bright light.

Use no abrasives... if it is really ugly use the point of an ordinary graphite pencil to smooth the mating surfaces.

If all else fails replace the socket.

Happy hunting!

Turn the parking light and compare the brightness on all lights. Next turn the flasher and compare the brightness on all light. Some time light bulb like 1157 will be insert the wrong way and short the light to signal. second open the light socket remove the bulb and inspect for burn mark and rust(replace the socket.
Behind the carpet is the ground point, clean and tight the ground.
and last is the combination switch for light and signals.
Good Luck

Check the display. Ask a helper to step on the brake pedal while you check the lights from the rear. If no lights appear, check the fuse that connects the brake lights. The owners manual will show the location of the fuse box and which fuse is for the brake lights. Pull out the fuse and look at the wire in the central window. If the wire is broken, replace the fuse. Make sure the new fuse is not blown, and carries the same amperage.
Take note of lights that are out, if any are working. The problem may be cured by replacing the bulb in a brake light that's out. A burned out bulb has a broken filament and a dark brown spot on one side. Check the owners manual for bulb type.
Check the circuit if replacement bulbs and fuses do not restore the lights. Find the wiring diagram in the vehicle assembly manual. The circuit for the brake lights runs from the battery to the fuse, to the pedal switch, to a connection plug, to the lights. The circuit has to be checked with a volt tester at all points.
Check the battery power and the light on your volt tester. Turn the ignition key far enough to activate the electrical systems. Turn on the lights to check for battery power. If the battery has power, ues it to check the volt tester. Put the black lead (the ground) from the volt tester on the negative battery terminal. Briefly touch the red tester light on the positive terminal. The light on the volt tester should flash brightly.
Test the wiring to the fuse. Clip the ground wire to solid metal near the fuse. Touch the light tip to both sides of the fuse. Both should light the tester. If neither side lights, the wire between the battery and fuse is bad. If only one side lights, the fuse is blown.
Test the switch and wiring. Touch the light tip of the tester to both terminals on the brake pedal switch without putting any pressure on the pedal. One should carry power and the other should not. When both show power, the switch is stuck and the brake lights are always on. If neither shows power, the wiring between the fuse and the switch is bad. Now check both switch terminals while the pedal is depressed. Both sides should light the tester. If not, the switch is bad.
Check the connection plug. Unplug the connection and refer to the vehicle manual to identify the brake light wire. Touch the tester light on the brake light wire at the inner socket on the battery side. If the tester lights, the power is flowing to this point. If not, the wire between the plug and the pedal switch is bad.
Check the socket. Plug in the connector plug and remove the bulb. Touch the contact inside the socket. If the tester lights, the socket is good. The socket and wire running to the plug should be replaced if the tester doesn't light.
Check the bulb with the ground wire. The bulb must be in its socket. The ground wire running to the socket should be black or brown. Stab the tester through the insulation. If the tester lights, the bulb is good. Replace the bulb if it doesn't light.
Check the ground wire. Remove some of the insulation around the ground wire. Twist one end of the extra wire around the exposed ground wire. Touch the other end to a solid piece of metal. If the brake light comes on, the ground wire is bad.
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is the socket that the light plugs into burned or green looking in the contact area if its green or discolored it needs to be cleaned if its burned change the plug there should be three wires 2 + 1- one + for low beam 1+for high check with a volt meter for voltage from 1 wire to frame ground and do the same with the other if voltage is present on both now you know which is the -plug the light in and jump a wire to frame ground if this was the problem it will work now also check for tightness of the bulb when plugged in good luck LATER MAN!

What did the dealer say? (QUESTION? do both the front & back (R) side lights burnout or just the front or the back light is burning out?) - 1. check for corrosion in both the front and back (R) side directional lights sockets. 2. Check to see that the fuse is the correct size, if a 20amp fuse is installed when it should be a 10amp fuse the lights could get a intermittent electrical spike that is burning out the light instead of the fuse. This doesn't help the problem, but it would tell you the problem isn't between the fuse wiring to the light. 3. One last thing I can think of is: some lights ground themselves when you reattach the plug to the chasse. NOTE: not all lights work this way, some other work just the opposite and have a fabric-washer around the top of the plug to keep them from grounding. Confirm what kind you should have as a precaution.

Sorry I couldn't be more helpful. Good Luck

you need to check for power and for ground at the lightbulb socket to determine which is not contributing to power the bulb(s). If the marker lights work at the rear then suspect a broken/melted light bulb socket, broken wire, or broken/rusted ground connection. Again, check at the light bulb socket for ground on one side (black wire) and 12V (brown wire) on the other. The light socket should have terminals that actually touch the light bulb; sometimes the sockets will melt not allowing a good connection. a cheap harbor freight multimeter (VOM) will help. Right and left side use separate fuses

You do not have a separate fuse for each side, if the left side works, replace the bulb in the right side that isn't working.

The running lights may be a bad relay or bulbs, if the bulbs are good then check the connections, make sure the socket is not burnt, if you remove the bulb the socket shouldnt have any melted area in it, also take a good look at the ground wire coming off the sockets, a quick test is to connect a wire to a good metal ground and then connect it to ground wire to a bulb socket if light brightings then you know its a bad ground, replace the ground wire or located the bad ground. hope this helps.

You either have a bad ground or the bad electrical connection at the light socket is "simulating" a bad ground. This is putting a high resistance on the bulb and it's taking it's toll by burning out the bulb. I would start with a new socket, and CHECK the ground. If you still have the issue, I would run another complete ground wire and not even worry about checking the ground itself. the Stick