2003 Silhoutte, both lower brakes lights do not work. Bulbs or turn signal switch? Turn signals work okay. Cyclops works okay, fuses look good.

Most of the time the problem is in the turn signal switch. The third brake light circuit bypasses the turn signals.
Someone would need to check brake light power in and out of the turn signal switch.

Well the brake light and turn signal circuits are on two different fuses, but they both go thru the turn signal switch.
So I would start by checking for power in and out of the turn signal switch for each circuit.

first check signal lights fuses if none of signal lights work.if fuse okay,check for burn out bulbs.if all is good turn signal switch is bad or you have loose wire to signal switch if your turn signal lights work some times.

check voltage from the brake pedal switch to the signal sight switch, center light is not on the same circuit, first clue is the signsl lights work so all the wiring from the switch is good, also power to the signal switch is good but not power from the brake switch

check the rear lower bulbs, if good nore than likely brake lamp switrch on brake pedal, 3rd lamp rns of separate circuit

This is a common GM specific problem. Your turn signal switch contains an elaborate networking device that has to cancel brakelights while running a turn light. Often times the ground within the turn signal switch is lost causing your situation. After investigating such other possibilities as fuses and loose grounds it may become necessary to replace the turn signal switch. Thank you, Dana

The brake lights are routed through the signal light switch.
Looks like that will be the next switch to replace and the problem.

This is a classic example of turn signal switch failure. On GM vehicles with a multi-function turn signal switch and combination stop/turn/tail lights (all rear lights are behind red colored lenses except for back-up lights) The brake light power is routed through the turn signal switch. This makes it possible for the right rear light to function as a stop light while the left rear turn signal flashes, and vice-versa. When the contacts fail to remain constant the brake lights, and turn signals can become intermittent. The proof that the brake light switch is functioning correctly is that the high center (cyclops) brake light functions properly. Wiring integrity is verified if you can prove that turn signals operate, but that can still be intermittent with this complaint, BUT if you use your hazard switch to turn on all the signals at once, you can verify wiring integrity. This is because the turn signal, and the brake light use the same circuit, and bulb filament in the rear lighting assembly. If any Hazard lights fail to function, check bulbs first, then retest. If all Hazrd light flash correctly and reliably, bulbs, sockets, and wiring have proven integrity, and the turn signal switch is the remaining component in the system which needs to be tested. Unfortunately, this switch requires disassembly of the steering column for service, testing or replacement. If you have never disassembled, and successfully reassembled a GM tilt steering column, I would reccommend professional assistance.

This is known problem, and it is the turn signal switch.