That sounds like a rubber hose breaking down. Could be coming from your fuel line or if you have a storage tank and hose, the storage tank / hose may be the culprit. I can't believe that it is the tractor fuel tank since it should be specifically designed to contain the fuel. If you have used some fuel additives, it could be some kind of chemical reaction taking place with a bad additive mixture or ratio.
If you use a fuel storage system, install a good fuel filter/water separator system on that so you get clean fuel to your tractor. Drain and flush your tractor, make sure any delivery hoses including fuel hoses on your tractor are rated for the type of fuel that you are using and you should be good to go.
I had the same rubbery type of gunk stopping up my hydraulic filters that it took 5 flushings/oil changes and filter changes to get rid of. I never had a fuel system problem like you described but I always use a 10 micron fuel filter on my fuel pump to make sure I get clean fuel.