Replacement Connectors
As long as the plastic connector body is reasonably intact you can repair the connections. The spade terminals have a small barb on the back side of them (opposite the curled side) that holds them into the connector body. Use A very tiny screwdriver from the light switch side of the connector to release the terminals. Best to do one at a time, so as to avoid confusion when reassembling. Now you can have a good look at each terminal, if they have turned black or the wire insulation has melted, or the wire is loose it will need to be replaced. It is possible to gently squeeze the terminal to make it fit a bit tighter, do one side at a time to avoid squishing the barb. Replacement terminals with barbs are available from Standard Motor Products, the ones that I have are part number SST99 and work up to #14 ga wire.
Nothing wrong with adding a relay, this might also give you the oportunity to separtate the trailer running lights as well, and for sure it will greatly reduce the load on the headlamp switch. Just remember to fuse the relay supply according to the running light conductor size.
Bosch has some nice relays with plug in sockets, the socket part number is 3334485008 and the relay is part number 0332019150 or 0332019151 both rated at 30amps. The Standard terminals listed above will work with the Bosch relay socket, or you can buy a bosch pigtail kit for the socket. The advantage of using the socket is that it makes replacing the relay just a plug in job, as well as providing a nice mounting, you can also stack a series of these bases together if you like.
When repairing automotive type wiring get yourself a good terminal crimper, avoid the stamped variety as most are not made to work with non insulated terminals. Soldering after crimping is the best way to ensure a good connection, especialy for wiring exposed to the elements. I also like to heat shrink every connection, it helps to prevent the wire breaking off from the terminal.
Neil