I just aquired a barn find Club Cart. Cleaned all the battery terminals ( had to replace a couple of ends) and noticed a little wire on a solenoid looking object. The wire has an oversize tube of insulation around it and is burned in two. 

The device has a sticker on it that reads "White Rodgers 36v coil and a 586 1177111 number. It is located in front of the batteries under the F/R selector area way down at the bottom. The wire in question looks like it goes across two of the 4 terminals on this thing.

Does this wire being burned in two mean that this device the bad? What does this wire do?

Thanks for any ideas.