Hi
You're right, often a dedicated plug/socket arrangement. The most common being a pair of sockets, of the type seen on Landrover dash boards for many years.
Like this example:

- parking light.jpg (22.94 KiB) Viewed 2426 times

- Landy Dash.jpg (501.53 KiB) Viewed 2426 times
Your one looks to have been fitted with the sort of connector usually used on Sound equipment, found on the back of a typical stereo system or even the TV, known as an RCA Phono connector.
The RCA Connector dates from the 1930s, so a perfectly legitimate connector to have been used, they just weren't usually used as a power connector, they were intended for audio signals. But the low amperage of a parking light would be perfectly within their capacity.
If I were you, I'd look around the house on typical equipment like TV, Sound System, Satellite box or similar, and with it switched off, just confirm that the connector fits. It certainly looks the right proportions.
Then find an electronics store to get one.
A few years ago, I'd have said your local Maplin, but they closed all their stores and went on-line only.
Online, you'll probably find yourself buying a pack of 4 or so.
https://www.ebay.co.uk/itm/361409121204