If it's dribbling mayonnaise that sounds it's like a drain from the air box. The crankcase breather can blow emulsified oil and condensation into the box, at this time of year the cause is probably just oil temperatures not getting high enough to evaporate the moisture but it is always worth checking coolant level to make sure.
To replace it you will have to lift tank and airbox, detach old pipe from airbox and then if you can attach the new pipe to the old pipe and pull it gently down through the engine and frame you should be able to follow the correct routing. Usually it is to one side so the drips from it are not directly in front of the back tyre. Strange how it has cracked and deteriated so much on a bike that age. Maybe it was too close to exhaust and the heat has focced it.
Many years ago I had a Bandit 1200 and the breather pipe from the airbox had a little bung in the end, every time I washed it I would remove the bung and get about an eggcup of fluid from it, a mate with same bike had never done it and I did his and nearly filled a jamjar, inside his airbox at bottom was wet through.