1984 750 interceptor loses cylinder

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What's the history of this bike--has it set up for a while before you got it, etc.?

Tank could have rust, trash or debris that is blocking the filter screens on the petcock tubes. Are you running on reserve or normal setting of petcock?

Do you have a clear filter on the fuel line, see if there is debris in the fuel.

Fuel pump could be gummed up if there is no filter in the line and it is not able to keep up at the higher speeds.

More advanced diagnostics to determine if it's a fuel issue: If you have some fuel tubing on the bowl drain fittings you can shut off key and petcock, open drain, catch and measure how much fuel is in each bowl. Compare the amounts to find if one is too low. Do it when cold or after running fine, then after it cuts out. If one is low then that carburetor is your culprit, if all are lower after than before, then fuel pump or tank supply issue (debris?). You have already determined that tank venting is not likely culprit.

Carburetors may need cleaning depending upon bike history.

 

Next time be prepared to check all cylinders for spark as soon as she quits. If your problem is NOT fuel-related, you may have a failing pulse generator coil, which will show up as no spark on 2 cylinders and usually only happens after engine reaches full operating temperature.

 

It's Normal. The fuel pump only comes on when the pressure drops in the line to the carbs. As the fuel level goes down in the bowls so do the floats which open the inlet needle valves. This relieves the pressure in the line and fuel fills the bowls until the floats close the needle valve. Pressure builds up in the supply line and shuts off the fuel pump. It's not a rotary pump but a rube goldberg solenoid clapper device...

 

Yeah, it seems like these pumps get pretty suspect after a certain amount of time, I have had issues with two different ones on my bikes.

 

Bypass the fuel pump altogether--run the output of the tank thru a filter and straight in to the fuel tee. Gravity feed with a full fuel tank should be good to go. If problem goes away pump is likely dirty. If problem remains, then carb floats may need adjustment to raise the fuel level in the bowl. But my money is on a dirty pump since you found brown crud in your filter, some of it got thru...

 

disassembly of the fuel pump is VERY easy. I'd take it apart, clean it, change the fuel filter too while you're at it.

 

Bad coils

I had the same issues on my VF700F. I replaced the coils and the rectifier. The bike would start and run fine to warm up. If I took it out for a 10 min ride it would shut down once it got hot. I would let it sit for ten min and it would get me home. One coil will cause your tach to jump. The other coil will cause your fuel pump to quit. I used Acell coils with great results. The rectifier was replaced and the temp gauge stopped jumping up when it was not overheating. It also made a huge improvement with the brightness of the lights.