I've got a new to me 2004 2166 I bought last month. I'm a shadetree mechanic, so when I bought it, it only ran with the choke half way out. Pulled the carb, cleaned it and no more problem. What I do have now (don't think it is related to the clean carb) is that when the tractor sits for a week, which is typical, it will not start. I pulled the fuel at the carb and nothing for about 20 cranks and then the fuel came out. Put the fuel line back on and no problems at all. Shut it down during the lawn mowing and start with no problem. Next week, same issue. So I replaced the fuel pump, thinking that perhaps it had an air leak in it and it couldn't pump up the fuel from the tank or something. No change. Same symptoms. I did not, however, replace the diaphram, only the mechanical/plastic parts.
See if manual can help you out, let us know how it goes. I know the years don't match up but give it a try. Have you replaced fuel filter? I use 93 octane fresh gas & quality brand fuel treatment [per instructions on bottle] in all outdoor power equipment.
I was just out in my shed today. Sorry, it's a 2186 with a Kohler Command 20.
I pulled the fuel line again and cranked it over to see if anything came out of the fuel pump. Not a drop. Started it with starting fluid and still nothing. I sucked on the fuel line to ensure no obstructions, change the fuel filter...nothing. So at this point, I think the fuel pump gave up the ghost. I removed it, manually pumped it and I get vacuum on one side and blowing on the other. I don't know how much is standard spec. Any other ideas outside of replacing the entire fuel pump, including diaphram?