The DEAD TEST 781220 and DIAGNOSTIC 586220 Tools are two different programs for testing your Commodore 64 and finding hardware faults.

The 586220 part (one side) of this cartridge is actually a standard 8KB Commodore 64 cartridge located between $8000 -$9FFF

The 781220 part (other side) of this cartridge is an 8KB Ultimax Commodore 64 cartridge located between $E000 - $FFFF

Some of the tests in the Diagnostic 586220 program need a harness. Please check the following websites for more information. 

Thanks to Jani and Sven.

http://blog.worldofjani.com/?p=164

http://blog.worldofjani.com/?p=879

https://github.com/svenpetersen1965/C64-Diagnostic-Rev.-586220-Harness