Fuel In Sump :-(

If this is the petcock that you have, you can read the positions in the image. I just did a google search for images of the fuel petcock, but I'm not certain that it's for your year. You could try the same until you find your specific petcock, or spend a few bucks on a manual. https://haynes.com/en-us/triumph/trophy/1991-2003

 

Hi
Fuel tap positions depend on year all of mine built, late 92, 94 & 99 are

pointer up 12 oclock = Prime
Pointer @ 3 oclock = ON
Pointer down @ 6 oclock = Reserve

Some earlier ones the pointer was set in a different position Forward / Up / Rear

Vacuum should shut off the tap @ On & Reserve.
Prime leaves the fuel feed on gravity feed

I suspect you have dirt / grit under one of the float valve/s tips leaving fuel to flood into the cylinder/s.

Float valve needles are available, but I think on the Mikuni's the valve seat is part of the float assembly, but, I could be wrong abot that ........... wouldn't be the first time.

 

That looks like the tap off the adventurer, thunderbird or legend

 

Have a chat with Sprint mfg for the needles and advice,

https://www.triumphparts.gbr.cc/product.php/7004603/


Can confirm oldyam, ie fuel tap position and the pic of the tap (hackdriver) is not the standard tap for your model, but who knows what has been fitted in the past.

If you need a workshop manual for your bike here is a link
https://www.dropbox.com/s/ia2hex5rw70pip4/Triumph T300 Service Manual.pdf?dl=0

and if its any use

https://www.dropbox.com/s/a67oymz7es51402/Triumph T300 Owners Handbook.pdf?dl=0