I've looked mine all over and there are no wires like that....
I hate to assume with electronics, but what i would do, is check for voltage on those wires with a meter ,, with the key in the ON and Start position. if they never have any voltage, i think they would be ground wires. of course if the 1 on the left goes to the right (starter side) side of the solenoid, it would only get power during cranking.
what i would do in this situation is get the model and serial number off the back of the mower (on a sticker, if it's still there) and see if you can get a hold of John Deere.