Brake warning light on?

It shouldn't. Tightening the cable should do the opposite as it should make it harder for the lever or pedal to move and trigger the switch to turn on the brake light. However, that light can come on if there is an issue in the brake system, including low brake fluid or an issue in the hydraulic brakes that allowed the transfer switch to move. Have you had any brake work done or are the brakes due for service so that the fluid could be low?

Nope. Just the opposite. When you have drum rear brakes, the shoe return springs pull on the cables which pull up the parking brake pedal. If the cables stretch over time, they can fail to pull the pedal all the way up. That keeps the red "Brake" light on.

There are some variations to this story, but basically every vehicle has at least two, and usually three switches that can turn the red "Brake" light on. One is that parking brake pedal. The second is a switch run by the "pressure differential valve". That lives inside the combination valve, right below the master cylinder. That valve shifts off-center to turn the switch on when a leak develops in one of the two hydraulic systems. On GM and Chrysler models that valve is spring-loaded to return to the centered position, but sometimes they stick and need a good hard jab on the brake pedal to break them free. That valve is not spring-loaded on Fords and can be extremely frustrating to reset to centered.

The third switch, when used, is a low fluid level switch in the brake fluid reservoir. When the fluid gets that low, it can be because there's a slow leak, but more commonly it suggests the front pads are worn out and are ready to be replaced. As they wear down, the pistons in the calipers move out to self adjust. Brake fluid leaves the reservoir and fills in behind those pistons.

When you don't know which switch is causing the red "Brake" light to turn on, it's usually pretty easy to unplug the low-fluid-level switch on the side of the reservoir. If the light turns off, check if the fluid level is really low. If it is not, the float has likely become water-logged and sunk. There's a magnet on it that trips the switch, which is a reed switch. If the fluid is low, we normally do not add any. Same is true when we top off fluids during other routine services like oil changes. When the front pads are replaced, we have to push the pistons back into the calipers to make room for those new, thicker pads. Doing that pushes all that brake fluid back up into the reservoir. At that time it will be near full again. If someone had added fluid before that, now it will overflow, creating a mess. The pressure differential switch can be unplugged too, but they can be harder to reach. It's on top, in the middle of a brass block on the driver's frame rail, right under the master cylinder. Follow the two steel lines from the master cylinder down to that block.

A hint for the parking brake switch; if you leave the engine off, ignition switch on, and the red "Brake" light is already on, watch very closely the brightness of that light as you push the parking brake pedal down. If you see a very slight increase in brightness, that's when the parking brake switch turned on, meaning it wasn't on at first. That can rule the need to add that switch to the list of suspects. That trick doesn't work with the engine running because the charging system makes the change in bulb brightness harder to see.

The bigger problem with an over-tightened parking brake cable is it will keep the rear shoes partially applied. The same thing can happen when the cables become sticky. Drum shoes are designed so the shorter "leading" shoe, (meaning toward the front of the truck), grabs the rotating drum and tries to rotate with it. That action pushes out on the bottom of the trailing, (rear) shoe. That's half the action that puts braking force on the rear shoe. It's longer because it is the one that does most of the stopping.

When the parking brake cable is too tight, it causes the leading shoe to grab violently with just a little foot pressure on the brake pedal. Very easy rear-wheel lock-up occurs causing skidding. The roles of the two shoes are reversed when backing up, so that sudden grabbing doesn't occur then.

There's another chapter to this sad story when the truck has anti-lock brakes. That's an add-on option that comes in two versions. Most trucks had rear-wheel anti-lock brake, (RWAL) systems. The higher-end version is four-wheel ABS. Both systems can detect various defects and set diagnostic fault codes. When that happens, the computer turns on the yellow "ABS" light, and it turns the system off. This also happens when the red warning light is on. The ABS Computer doesn't know why the red light is on. It only knows it's possible it's on due to something that will prevent the ABS system from functioning properly, so it turns the ABS system off.