Welcome to the forum Alan.

I used to have a 3YF myself back in the day!

The pipe (and it should be a pipe) you're talking about is the float bowl overflow. If fuel is spilling out here then you've probably either got: (a) A punctured or split float that's not rising enough to close the needle valve, or (b) Some crud/grit/dirt preventing the float needle from sealing/seating properly.

Buy yourself a gasket/seal set for the carbs and strip and examine the float bowl and check the float/needle operation.

One of the most common problems on these bike's are the way the seals, gaskets and floats get tired and fatigued with age, particularly as the twin carb setup is fiddly and tends to get neglected on older bikes. You'll be really pleasantly surprised with what a relatively cheap to do carb "freshen up" will achieve. You'll wish you'd done it years ago.

BTW - As has been pointed out, we're mainly about the fuel-injected 660s here. You're more than welcome of course, but the place you need to visit for info on the 5-valve Tenere is:

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