We can't find the exact model where we live, but I think if I can identify this socket we can find an equivalent.
The generic name for this type of connector is "circular standard connector" and it's waterproof by virtue of its screw-tight outer ring. This one has 2 pins but multiple pins are available - I recognize it because 3- and 4-pin variations are used in addressable LED christmas light displays.
Searching for "2-pin circular standard connector" shows me several that have different keying than your images (the flat part that makes sure you can only insert it one way) so I'd say this may be harder to find than you think.
If you have a good heat source you might have an easier time replacing the power supply and butt splicing a different, more standard connector to your lighting.