I have an odd issue going on with my 73 DT3.
Last spring--cleaned the fuel tank.  A LOT.  I cleaned, two other people cleaned, it looked pretty decent. 

It is still emitting teeny tiny specs of stuff.  Plugged up one fuel filter already.  New one is nice and pretty clean.  Today I ran a bit of fuel into a nice clean sour cream cup and she looked like new gas to me.

Bike goes from running good to running like crap.  Then back to good.  Depends on it's mood.

The fuel tap/petcock was taken off and gaskets redone on the inside.  The tube going up is not intact. 
Bike goes below 3/4 tank, starts running like crap.   Full tank?  Starts just about right away.  No problem.

How critical is that brass tube in the fuel tap?  
I have a spare aftermarket one I can try.  Would an "original Yamaha" NOS tap work better or be less problematic?

I apologize for the questions.  

Seems there is a plugged tube then... well, dirty.. Should have any issues with main or reserve.. Are you able to remove it from the bike and use some wire to insert in each tube... the use compressed air to blow it out from both directions? You may need to disassemble the whole petcock for a thorough cleaning.. and verify its up to par..
Sneezles61

How well does the tap flow if you let it go for a minute into a clear glass jar, & how does 'on' compare to 'reserve' for flow. Does it flow constant into the carb--remove the side main jet to observe flow--but makes a mess. Oring on the jet setter is important to seal but would give a constant rich fault if it was 'that'. My first thought for performance that comes & goes is the exhaust, & loose carbon lumps blocking the spark arrestor then dropping away. Reading back though i guess you're onto it with dirt in the tank & tap. Is the fuel cap breathing enough. Can test that by constant flowing the tap into the jar trick!!. Can you run it on reserve from full to empty to see if it varies. Sorry if i'm not making sense--keep getting interrupted here.

 

For now I mounted up an aftermarket one with plenty of fuel capable gasket sealer. 
I think the original fits better.   
you can see the brass tubes were badly damaged over the years.. one was a nub,, and one was maybe a half inch long... part of the problem...
if I were to order some brass tubes, how long?  They appear to be about 7 mm and just press into place. 

 

If you can order brass tubes... Does it matter if ones a couple inches and the other is a quarter inch?.. As long as the on and reserve are observed..  Be a sad day to run out and find that the tubes were opposite of what they should be.. But.. keeping the reserve  slightly above the bottom of the tank will also help keep bigger grains of sand out of the system.. perhaps..
Ssneezles61

On had a brass tube probably about an inch or more long.  Reserve had a plastic filter screen thing to try a keep the bigger chunks that settle in the tank from getting into the filter.  Some early bikes reserve was just flush with nothing.

Something like this looks pretty good quality. Could easily shorten the brass on position tube to the desired length but be careful pulling the filter off the tube & re-fitting.

One problem solved. Original tap, I found an 8mm brass brake line.  It was perfect. Should have snapped a picture.  I cut it to stand 45 mm above bottom.