What does the turn signal module look like and its location?

It doesn't have one. It is electronically switched by the BCM. It does have a relay for the 4-Way Hazard lights according to the videos.

2006 MALIBU ls: THE LOCATION OF THE TURN SIGNAL ...

JustAnswer https://www.justanswer.com > Chevrolet Repair
Sep 13, 2008 · 1 answer
Welcome Customer You car does not have a standalone flasher module, rather the BCM is responsible for controlling the blinking of the lights.

https://www.google.com/search?q=flasher+located+on+a+2006+malibu

..

There isn't one. The function is done by the Body Control Module (BCM) along with lots of other functions.

Where is the turn signal relay on a 2006 Chevy Colorado?
The turn signal is controlled by the BCM (Body Control Module) that is located at the passenger side kick panel.
May 21, 2014

2006 Colorado turn signal relay? where is it - 355 Nation

Known issue

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Doesn't have a turn signal flasher , use's lighting control module .
Turn Signal and Hazard Lamps The turn signal system consists of:

• turn signal miniature bulbs (13465).
• turn signal indicators in the instrument cluster (10849).
• lighting control module.
• multi-function switch (13K359).
• circuit wiring and circuit protection.

Power is supplied to the lighting control module through instrument panel Fuse 6 (10A). This fuse is hot in START or RUN. The lighting control module is connected to the turn signal switch portion of the multi-function switch. Ground is provided to the lighting control module and the turn signal miniature bulbs through Circuit 57 (BK).
Turn signal functions are performed by double filament bulbs in lamp assemblies located next to the headlamps. The turn/hazard function uses the second filament of the appropriate bulb(s).

• With the multi-function switch in the right turn position, power is supplied to the RH front and rear turn signal miniature bulbs and the right turn indicator in the instrument cluster.
• With the multi-function switch in the left turn position, power is supplied to the LH front and rear turn signal miniature bulbs and the left turn indicator in the instrument cluster.

signal light control module LM487 ???? How did you come up with this ??? Your vehicles BCM - body control module controls the hazard an turn signals . Turn Signal/Hazard Lamps
When the turn signal switch is placed in either the left or right position, a ground signal is completed from the turn signal switch to the BCM. When the hazard flasher switch is activated, a ground signal is completed from the turn signal/hazard switch to the BCM. The BCM then sends an ON-OFF voltage signal through the fuses to the appropriate turn signal and side repeater (export only) lamps or to all of the turn signal fuses for hazard operation. The driver door switch and passenger door switch also receive voltage from the BCM turn signal supply voltage circuits for the mirror turn signals. The door switches have no function or control of the mirror turn signals other than a pass through connection for the circuits. The audio chime is also activated when the turn signals are ON. The instrument panel cluster (IPC) receives the signals to activate the turn signal indicators over the GMLAN serial data system. When the hazard switch is pressed, all turn signal lamps will flash including both IPC turn indicators.
Your best bet , take it to a qualified repair shop .

The turn signal module (TSM) is an electronic microprocessor that controls the turn signals and four-way hazard flasher. The turn signal module receives its information from the speedometer and turn signal
switches.
On models equipped with a security system
(TSSM), it is incorporated into the TSM module. The
bank angle sensor (BAS) provides motorcycle movement
signals to the module. TSM and TSSM modules are not
interchangeable.
The turn signal module, TSM or TSSM, is located on
the electrical panel located in front of the rear wheel.
When there is a problem with either system, a diagnostic fault code(s) is set. The TSM or TSSM can only be tested with Harley-Davidson diagnostic equipment. If any portion of the module is inoperative, refer the testing to a Harley-Davidson dealership

It could be that one of the flasher module for the turn signals is bad. There should be 2 flasher modules: one for turn signals, and one for four way flashers. Check you vehicles manual for a location on the flasher modules, or Google a query like "Location of turn signal flasher module on a *Year Make Model*". After you locate them, it should be as simple as going to an auto parts store and asking them for a replacement module. If that doesn't work, I could be the switch in the dashboard, or a more complex wiring problem. Make sure you check all of your fuses too. I would say that if you cant fix it by replacing the flasher module, you should take it to a mechanic because it is very easy to destroy wiring in your car.

That model I believe the turn signal module is located under the fuel tank to the front of the bike.

The modual is the trun signal it's self. Other than that it runs through the BCM and that distributs the power to the lamps.
Do the indiactors on the dash light up at all? Or do you just hear a clicking noise?

Turn signal flasher module is behind dash left of steering column near chime module. I have a 94 Seville and I had that same problem you need a Turn Signal Flasher Moduel, I forgot the proper term for it but I had to get mine replaced too. When I hit the signals to turn the side light would come on but the signal light wouldn't. Its a little box you get from Cadillac it only cost like $20 - $25 and you get it installed and trust. It'll work again. I just got mine done this week and my car now has turn signals again.