When dim head light is turned on, right side brake light is on with high intensity. When brake is applied, the right side brake light is still on. Meanwhile left side brake light behaves normally-dim head light on, left brake light low intense on; when brake is applied, high intense left brake light turns on.

Headlamps
You can use the headlamps two different ways.
• Place the headlamp switch in the HEAD position for normal operations
• Place the headlamp switch in the OFF position for automatic lamp control (ALC) operation. During ALC the low beam headlamps are ON for daytime running lamp (DRL) operation in daylight conditions at reduced intensity or low beam headlamps ON at full intensity with exterior park lamps ON in low light conditions.
The body control module (BCM) applies a pulse width modulated (PWM) voltage to the headlamp module and high beam relay in the underhood fuse block. The ground for the headlamp module is supplied from G113 or G115. For normal manual low beam operation when the headlamp switch is place in the HEAD position, ground from G202 is applied through the headlamp switch and to the BCM through the headlamp switch headlamps ON signal circuit. The BCM then applies a PWM voltage to the headlamp module/high beam relay voltage supply circuit. The headlamp module then applies battery positive voltage through the left front (LF) and right front (RF) LO Beam fuses to the left and right low beam headlamps. The ground for the left headlamps is supplied by G101 and the ground for the right headlamp is supplied by G100.
For high beam operation, ground is applied at all times to the headlamp dimmer switch from G202. When the headlamp dimmer switch is placed in the HIGH position, ground is then applied through the headlamp dimmer switch signal circuit to the BCM. The BCM then applies a ground to the headlamp high beam relay control circuit. This energizes the HI Beam relay, the relay then applies battery positive voltage through the LF and RF HI BEAM fuses to the LF and RF high beam headlamps. The ground for the left headlamps is supplied by G101 and the ground for the right headlamp is supplied by G100.
The BCM then sends a class 2 message to the instrument cluster in order to illuminate the high beam indicator lamp. If the headlamp switch is left in the HEAD position, the inadvertent power control feature will turn OFF the headlamps after 10 minutes after you turn the ignition switch to the OFF position. If you place the headlamp switch in the head position after the ignition switch has been turned OFF, or if the ignition switch is in ACCY position, the headlamps will remain ON until you turn them OFF or until the battery runs dead.

Low Beam System Operation
The headlamps may be turned on two different ways. First, when the end of the of the turn signal/headlamp switch lever is turned to the second detent position, the headlamps will illuminate. A ground signal is provided to the DRL control module. The module then provides a ground path to the coils of the HLP relay. Since the head relay is provided with battery voltage to both the contacts and the coil, the coil becomes energized and closes the contacts providing voltage to the DIM relay. With voltage and ground provided, the low beam lamps light. Second, with the switch in the OFF position, for automatic lamp control (ALC). During ALC the headlamps will be in one of the following modes of operation:
• Daytime running lamp (DRL) operation in daylight conditions, refer to DRL below for the operation of the circuit.
• Low beam headlamp operation in low light conditions. When the ambient light sensor senses a low light condition for approximately 15 seconds, it will cancel DRL operation and turn on the headlamps at 100 percent intensity. A path to ground is provided to the coil of the HLP relay. With a direct path to ground provided to the headlamps though the DRL control module, the headlamps will light at 100 percent intensity.
High Beam System Operation
The high-beam headlamp operation is controlled using the turn signal/headlamp switch lever on the steering column. In order to change headlamp operation from low-beam to high-beam, push the switch lever toward the instrument panel (until the detent is felt) and release. With the switch lever in the high beam position, ground is provided to the DRL control module through the turn signal/headlamp switch and splice pack 200 to G200. The DRL control module provides a ground to the coil of the dimmer relay. Since voltage is being applied to the dimmer relay coil, it becomes energized. Voltage is then applied through the closed contacts of the dimmer relay and the to the high beam lamps in the headlamps. Since ground is provided to the headlamps through the closed contacts of the energized DIM relay, the high beam lamps light. The high-beam indicator (blue) in the instrument cluster will light during high-beam headlamp operation. In order to change headlamp operation back to low-beam operation, pull the turn signal switch lever toward the driver (until the detent is felt) and release.Your best bet , take it to a qualified repair shop.

check for bad ground wire connections

If those lights all worked properly before the shop "fixed" it, take it back to the shop and ask them to make it right. If they are reputable, they will correct the problem(s). If not, think Small Claims Court.

It can be loose wiring or issue with bulb or the battery is weak or brake light socket getting short somewhere.Car lights getting dim,there are many such common issues noticed.I will share some familiar help links,related to your problem.
Click the link below:---2004 Dodge Ram: High Beam Light is DIM? http://technoanswers.blogspot.in/2012/04/2004-dodge-ram-high-beam-light-is-dim.html
----------Ford Odometer Dims intermittently http://schematicsdiagram.blogspot.in/2012/07/ford-odometer-dims-intermittently.html
---------Turn Signals Don't Work When Brakes Are Applied? http://schematicsdiagram.blogspot.in/2012/04/2005-gmc-envoy-turn-signals-dont-work.html
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Brake light Switch Location? http://schematicsdiagram.blogspot.in/2012/04/1996-buick-regal-gran-sport-brake-light.html
----------- No brake lights on Buick? http://schematicsdiagram.blogspot.in/2012/04/no-brake-lights-on-buick.html
----------- Brake lights not working on 1989 BUICK REGAL? http://schematicsdiagram.blogspot.in/2012/04/brake-lights-not-working-on-1989-buick.html

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These will help.
Thanks.

More than likely a bad ground in the wiring harness's. Have you changed your transmission, Alternator, or starter? Or added a trailer plug on the bumper?

it could be a bad connection in the stoplight wiring most likely the earth wire check all the wiring connectors to make sure they are plugged in properly.....hope this helps.....cheers

was this with a trailer connected or was there recently been trailer wiring added?

the tail light and brake lights are working from double contact bulbs. check the grounding, you dont have enough ground from one of the bulbs

Chk. for poor ground to headlights.