I can't come up with a schematic, but may be able to help-
IF this tractors head lights ONLY operate when the engine is running, you have a nominal 3 AMP DC charge system and a 70 WATT AC lighting system.

The charge system uses a diode to convert the AC output of the alternator to pulsating DC for battery charging.
Many of these systems have 12V to the diode from the key switch, with the assumption that current won't flow back through a GOOD diode.
Your diode has apparently gone bad and has some degree of "leakage".

Click the link for the "go to" diode that people use for an inexpensive replacement.

Here is a link that might be useful: Diode

You have a Kohler CV16S engine and this should be your engine charging system wiring diagram.

You need to find the wiring diagram for the Scotts 1642 so we can see what JD did on chassis. Found this posted on another forum and it looks like it uses the diode...

http://www.tractorbynet.com/forums/parts-repairs/279539-wiring-diagram-needed-s1642.html

If you undertake the repair yourself REMEMBER, diodes are directional

This post was edited by justalurker on Thu, Jul 18, 13 at 0:52