If your Mustang won't start,...
If your Mustang won't start, check the condition of the battery terminals first. Many times cleaning the posts and cable ends will fix it.
If the test bulb does light, the problem is either the starter solenoid, the battery, the starter, or any of the connections. You'd be surprised how many times I've solved this problem by removing the battery cables to clean its posts and cable ends. Above all else, the battery cables and posts need to be clean and tight. The best tool for this is a post cleaner you can buy at any auto parts store. It has a wire brush for cleaning the inside of the cables and a circular wire brush to spin on top of the battery posts. Install the cables and make sure they're tight. Now try to start your Mustang.
If that doesn't cure the problem, check the battery. Measure the current from the positive side to the negative side with a voltometer. If the voltage is below 12V, the battery needs to be charged or replaced. With a charged battery, the car should start.
Battery Not Charging
Checking your charging system is an easy task. All you need are the tools to remove the battery cables and a voltmeter. The first thing I check when a battery isn't charging is the current draw. To do this, remove the positive cable from the battery, then connect a voltmeter with the red positive clip touching the battery positive post and the black negative clip touching the removed positive battery cable. The voltmeter should read 0 volts. If you get anything close to 12 volts, something is turned on or shorted, draining the battery as the car sits.
Next, make sure the battery is receiving a charge from the alternator. Start the car and connect the voltmeter with the red clip touching the positive battery post and the black clip touching the negative battery post. You should see from 13.5 to 15 volts. If it's less than 13 volts, the alternator or the regulator is at fault.
One thing to remember about the charging system: never remove battery cables from the battery posts while the engine is running. This can blow a diode in your alternator or cause other problems. Some people use this method to see if the alternator is working. Don't do this. If you get the 13.5 or so volts at the battery while the engine is running, the alternator and regulator are working.
Bad connections can often cause the signs that indicate a component problem. Over time, the fuse panel can get rusty or the tabs that hold them fatigue and the fuses don't make good contact. If the holding tabs are rusty, they need to be wire-brushed, then treated with a cleaner such as WD-40. I've solved a number of problems by popping the fuses out of the holders, spraying the fuse panel, and reinstalling them. If the holding tabs don't hold the fuse tight, they can be gently bent closer together to hold better. When spraying the panel, I coat the backside as well. Be sure the battery is disconnected.
Every now and then I come across a fuse wrapped with a chewing gum wrapper or aluminum foil. This isn't a solution. If a fuse is blowing, there's a reason. Without the protection of the fuse, a wire or wires in that circuit can get too hot and melt, taking other wires with it. Find the problem and fix it or leave the fuse out until it's fixed.
Connectors themselves can become loose and not make good contact. Sometimes I take a thin knife blade and slightly bend the terminal to make it tighter on the component. Other times, I use a pair of needle-nose pliers to gently squeeze the terminals together.
This sort of goes along with bad connections. As I mentioned earlier, a circuit is the flow of current from the battery to a component, and then to ground. If all goes well up to the component, a bad ground can make the circuit incomplete. Some things ground through the wiring harnesses. The harnesses have ground wires and ring terminals strategically placed throughout the car. Some things, such as taillight-bulb sockets, ground to the metal where they install. Just make sure the surface is clean and free from rust or paint.
Fuse-panel tabs need to be...
Fuse-panel tabs need to be clean and tight to make good contact with the fuses.
Flickering Dash Lights or Headlights
Other than faulty connections or a bad alternator, sometimes this can be caused by a low battery. If a battery isn't holding a charge, the system keeps trying to charge it. Check the battery first and you may find the weak point.
Sometimes the headlight switch can be the cause. It contains an internal breaker that can get too hot and fail, causing headlights to flicker or go out. The lighting system is the hardest draw, designed for the headlights of the day. Today's halogen headlights are brighter, pulling more power and stressing the system. You may want to consider installing relays on the headlight circuits.