I have an 87 Mustang GT 5.0..

never heard shorts were common.

What is your battery voltage ? when is the last time you changed the rotor, and distributor cap (tune up)?

I actually just bought the car about 2 weeks ago and the battery came out of a 91 Ford Taurus Stationwagon from what I was told. But yeah, I have no idea about the others...I heard there is a way to test this by the two wires running to the distibutor.

This thing has bad problems.

the 5.0 is a solid engine design, should be easily fixable. spark is hard to see in the daytime, if you had a timing light, you could see it better. typically when getting a used 5.0, I change out the fuel filter, rotor, rotor cap, sparkplugs, check the battery (usually have to replace it), and check the timing, and check compression, check for loose hoses, or decreped hoses, your 87 should have replaced most of the small hoses by now(vacuume leaks). If you have the time and tools, pull the spark plugs and "read" them, they should be whiteish, very black and oily could be bad news. (google for it) Fast car when you get done, and very cheap too.

I would do a compression check on it first, read the plugs, before sinking a lot of money into it. you could have a burnt valve etc. Car doesn't have to run to do these things.

Does the tach bounce when you crank it?

If the TFI module is bad, it wont bounce while cranking but will bounce once as you switch key on. other possibility is the distributor pickup.

And they arent 100 bucks if you can change it yourself. About 45 bucks including the special wrench - sold separately.

Make sure to put clean heat sink grease on it, scrape the old off.

The Ford "cease fire" ignition module is famous for failing without warning on your vintage Mustang. Just about any autoparts store can provide you with a more reliable replacement for a lot less than a C note. Don't forget to buy the funny little installation tool, it saves a lot of aggravation.

"vintage"?