I'm no expert, but it looks like the return dreck-link feed. The other end should be connected to the hockle-rotor assembly. If it comes loose the window mechanism doesn't work. Oh, and always keep the nipple greased.
Sketty, they are all taking the piss out of you, I worked in a garage for 10 years, that thing there is the inlet valve to the sprocket flange.
You need to grease both your nipples in order for a big end to glide freely into your gasket, this will keep the pistons lubricated & prevent the ball joint from seizing up, you must also make sure your front bush is free from dust & dirt as this may cause a misfire when going at full speed ;)
They're still all taking the piss because I'm pretty sure the hockle-rotor assembly was replaced by an orbital gimbal starting in 1963. And of course the sprocket flange is under the back seat, not in the door.
Most likely the purple tube is a sleeve around the torsion cable from the window crank, and the cable has broken and fallen out, leaving just the sleeve.