What makes the security light come on in a 1999 Chevy Tahoe and sometimes won't start?

The car won't start because of the security system. The security system will either have to be bypassed (there are kits available on Ebay sometimes and there are some websites that have them too) or replaced. The ignition key has a built in resistor that the security system checks when you try to start the car. If the security system doesn't recognize the resistance of the key it won't start the car. Then you have to wait 2 to 10 minutes before it will start ( sometimes it's a lot longer than 10 minutes). You could try getting a replacement key and see if the security system recognizes it better. GM installed security systems in their vehicles that are called Passkey I, II and III. So if you get a kit you have to know which system is in your vehicle.  more