Does your multimeter check amps? If not do you have access to an amp meter?
A voltage reading is not very useful. The voltage meter is subject to inaccuracies from corroded wires and such. Voltage can best be compared to the pressure in a water hose that is spraying out of the end. A large hose will experience less of a pressure difference than a small one so the results are dependent on many other factors. The amps are best compared to the number of gallons that flow through the hose and splash on the ground, this can be accurately measured and compared regardless of pipe size (wire gauge). Finding the parasitic loss is very difficult with just knowing voltage (not impossible, but you'd have to take wire size, wire length, resistance, etc. into account).
I know that the monochrome gryphon pulls around .05 amps but the new color ones might pull a tiny bit more. This is not enough to show a 4 volt drop in ANY standard automotive wire you have access to.
Here is what I would look for...
Check the pins of the OBD port. Wires wiggling in there causing all kinds of crazy issues are not unheard of. An easy way of troublshooting this is to get a reading of the amp draw on the cigarette lighter loop with everything plugged in as usual. Then unplug the programmer to see what the amp difference is.
Next would be to check the connections on the cigarette lighter and everything else on that wire. If there is a wire wiggling out it could easily touch bare metal and kill your battery charge or pull enough amps to give you the voltage drop you are seeing. Check for worn wires while you are going through connections since they can do the same thing.
Also, what is the condition of the battery? When some batteries get old their amp capacity begins to suffer which is closely followed by a voltage drop.
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