2 white wires and 2 black wires? That is most likely the "Brake/Clutch safety interlock" SWITCH.
The 2 white wires serve the starter solenoid circuit and the 2 black wires serve the engine kill circuit.

If you post the full technical model number found under the seat you have a better chance of confirming this. Number typically begins as 917 with a 5 or 6 digit # string following that.

Tractor is most likely a 917.275240, 917.275241 or 917.275242.
Those are the only 3 DGT 4000's I'm aware of and a RARE breed.
It does have the Kohler Aegis engine correct?

Tom is most probably correct, but this tractor has a little quirk to itself.
It has a temperature light relay. (bottom of the schematic in the OM)
This relay has 5 pins, but only 4 wires to it.

It does have 1 White wire
2 that I ASSume are Black, since they are ground.
1. undetermined.

Remove the burnt device and count the terminals.
IF it has 5, it's a relay.
IF it has 4, it's the clutch brake SWITCH (as Tom mentioned.)

The relay will have terminals marked, 30, 85, 86, 87 &87A.
Your electric parts list in the OM doesn't even list it, but it should be basically the same thing as the OPR listed.
Simply a Bosch relay used as a headlight low/high beam, horn etc. relay for many years.

I have absolutely no idea where it's located because I know little about these things.

Here is a link that might be useful: Bosch Relay

Forgot to mention-
IF it is the clutch brake switch-
1 White wire will come FROM the PTO switch and the other will GO to the starter solenoid. (small terminal)

IF it's the temperature relay, the undetermined color wire (possibly white) goes to the temperature LIGHT.
This relay is ONLY activated when the engine is cranking in order to "test" the temperature warning light.

OOPS!!! That was Mownie, not Tom P. Sorry Mownie!!!

No problem Fred, I get mixed up a lot myself. :^)