Small Engines (Lawn Mowers, etc.): Tecumseh 3hp engine not sparking through spark plug, point style, new spark

Question
1. With tester the spark shows when shorted to ground but when going  through the spark plug there is no spark showing in the tester or spark plug - what may be wrong?
Information
A.  New spark plug used.
B.  Engine is old and has been sitting around for a while.
C. Changed to another used coil believing it was in good condition (same results as original problem)

Answer
Do you have a point style ignition or solid state?

Section 8 covers ignition systems.

http://www.cpdonline.com/692509.pdf

If you insert the spark plug and then ground the tip of the spark plug do you have spark?

FYI, I have never had weak magnets and rust has very little to do with the ignition performance on basic mower engines.

Eric