I think you found the answer.  

Thanks for the response. I found a diagram + keys which was helpful. It appears my Mini should have a 2 pin flasher unit but someone has rigged it to work with the older 3 pin unit. The red wire between bridging 2 of the pins seems to power some of the dashboard as well as the after market voltage gauge. Surely this shouldn't be the case?

Check your wiring diagram..mine is older but I have five wires coming out. Wiring diagram. Where is the guy who’s tagline says you can afford the car you can afford the manual

New Mini owner here, it's a 1990, picked it up a couple days ago. My right hand turn signal has been unreliable and upon inspecting I've stumbled upon what I think is a previous owner's creative wiring.
Picture: https://i.imgur.com/BIa1v7e.jpeg
For some reason there's this red wire running from one connector to the other. This was held together by electrical tape, it got quite warm too.
Now with the ignition on my left hand turn signal will work fine. The RH turn signal however will not. I can hear the repeated clicking noise but all that happens is that the battery and oil warning lights will dim repeatedly. If I remove the red wire the battery and oil lights will extinguish.
Any ideas what's going on here? Is there any reason why those 2 connectors on the flasher should be connected?