I haven't tested a tach using a battery charger myself but I have repaired Mopar tach's and tested them with other methods.

So here is what I would do:
-Connect a +12 volt source to the long stud (the normal +12v input to the tach). This powers the tach circuitry.
-Connect your 12 volt source ground lead to the tach metal case somewhere.
-Connect battery charger + lead to the tach input terminal where the gray coil lead normally goes.
-Connect charger - lead to the tach case somewhere.

If I had a Mopar tach handy I would have tried this before posting. Sorry.

EDIT:
Re-reading John's post I believe he is saying to connect the charger's + lead to both tach terminals (where your blue and gray wires connected). This will power the tach AND supply an input signal by going to both terminals. Connect the charger black negative wire to tach case.

Let us know.