Trailer plug or socket fault?

I'm posting this as I know a bit about electronics but they are definitely not my strong suit.

Having never towed with the Passat since I bought it, last week I needed to use my trailer so hooked it up to the tow hitch and plugged in the electrics, only to find them not working. After a bit of wiggling the connector around and having to pull it out slightly it made a connection and the lights worked, but it is very temperamental and after driving a while they stop working.

What I want to know is how to test if the loose connection is in the trailer plug or the socket on the tow hitch? And also if the plug had been exposed to the weather (which it had) then if it is just a case of corrosion on the pins could that be cleaned up or would a new plug be absolutely necessary?

Please excuse my ignorance!! Thanks.