Hi,
At he rear of the petrol tank there is a small diameter pipe, I think it is a drain line of some sort. This pipe has a plastic t-piece fitted to it that has no cover over it.

Can someone tell me if this open end of the T-piece should be blanked off with anything.

If you are talking about the pipe underneath the rear of the fuel tank on a Superfour there are two, the larger one is for the drain from the filler recess the small one is the breather pipe for the fuel tank both should have rubber pipes connected to them and these should be routed down through the frame and exit just behind the gearbox it is essential that this is kept free of dirt to enable the tank to breathe while the engine is running otherwise a vacumm is created in the tank and this will stop the engine running.

What bike and a picture would be handy