Only with the engine running? Or also if the engine is not running?
If you use the Triumph parts book for your bike -
https://partsbooks.britishonly.com/partsbooks/20-10182C.pdf - this picture is shown on page 14. There, in addition to tube nr.8, the hose to connect is nr.33. This hose is very difficult to connect to tube nr.8 with the engine in the frame; try to buy hose with a very stiff wall so you can push on it and it does not collapse. Or you might have to remove the bike's fuel tank and battery and lay it on an old mattress to allow access to tube nr.8.
This picture is page 56 of the Triumph parts book.
In the parts list on page 57, part nr.17 has "
Part No." E5370 and "
DESCRIPTION" '"T" piece'. If you enter "triumph 70-5370" into the internet search you normally use, images (and links to sellers) of part nr.17 as drawn are returned (the image in your post #5 is of a later part).
If you look in the Triumph 1963-1970 650 Workshop Manual -
http://classicbike.biz/Triumph/Repair/1970s/70-Triumph-Repair-Manual-63-70.pdf if you do not have it - on .pdf pages 130 and 131/manual pages E5 and E6 are two drawings showing the connection of part nr.17 to hoses nr.16, nr.18 and hose nr.33 from the engine. If the oil tank vent on your bike is to the rear of the filler, part nr.17 and its hose connections are simply positioned to the rear of the oil tank.
Your bike might have clips for hose nr.18 inside the right hand edge of the rear mudguard; if it does, hose nr.18 should end just below the mudguard's rear edge.
If the mudguard does not have clips, hose nr.18 was routed under the frame tube under the seat, part nr.19 was attached to one of the bolts attaching the "Lifting handle" to the mudguard - parts book page 62, "Lifting handle" is part nr.36, bolts are part nr.16.
Hose nr.18 was then routed between the mudguard and part nr.43, ending just below the bottom of nr.43.