Is this a really old vehicle? Sounds like the ballast resistor has failed. I had this with an old Vauxhall Nova and replacement of the ignition coil cured it. The ballast resistor was built into the coil on that model.
It is normally located close to the ignition coil in an exposed position, so that it can transfer its heat easily to the air.
The purpose of the ballast resistor is to drop the nominal battery voltage down to approximately half its value for ignition coil operation.
A ballast resistor primarily refers to an engine component that lowers the voltage after starting the engine, since the voltage required by the engine drops significantly after starting. It is an electrical resistor that affects the voltage supplied to the ignition coil.
The ballast resistor makes the engine much easier to start by also doubling the voltage provided to the ignition coil when the engine is being cranked. Not all automobile engines have ballast resistors.
ChicksFan, September 2011