Sorry to read about your dad,

my condolences.
pipe going from the engine that T's off to the oil tank and out the back over the side of the rear
wondering what it does
Not copper, plastic discoloured by oil.
The crankcase (lower part of the engine) vents into the primary chaincase (left hand side of the engine), that short pipe to the oil tank
vent T and the longer pipe around the fender to the rear of the bike vents to atmosphere at the rear of the bike.
The plastic pipe has become discoloured by oil vapour vented from the primary and the oil tank. The slope of the pipe in that position means any oil that condenses in the pipe drains back into the primary.
pipe going from the engine that T's off to the oil tank and out the back over the side of the rear. my has broken off where it connects to the engine
wondering
what its called so i can go about replacing it.
Good to know part numbers when phoning/emailing parts sellers or searching for parts online.
71 Triumph 500 parts book, click this link for a free to read online copy:-
. Go to pdf page 68 (page 64 in the original paper catalogue), the part you want is #33, part # E11149 "Breather vent pipe".
. If using your computer to search online for sellers with a part in stock:-
.. Most use the 73 onwards part # format - same last four numbers but the letter and any first number of five converted to a numeric prefix. Sounds more complicated than it is, because there are not many different prefixes. In this case, the 73 onwards part # is 71-1149.
.. Also add "triumph" in the search string.
If you like manuals on paper, the parts book and the
Triumph workshop manual are still printed and available brand new from parts sellers.