Thank you all! I was out fiddling with it last night. And "fiddle" is about all I can do because I'm not much of a small-engine guy.
I held prime down for 30 secs, at the genset (not inside) and I could hear clicking and eventually smelled gas.
So, although I didn't yank the fuel line from the carb and actually see gas, I thought the fuel pump might be working.
While cranking, I yanked on the two wires at the top that connect to the carb. I'm guessing one could be a choke? Not sure what the other one could be, throttle?
Anyway - I was able to get it to catch and fire and run for about 5 seconds by pulling those wires. But 5 seconds was about all I could get.
The meter says 27 hours on it, so clearly someone had it running before me.
I'm thinking I really need to check the fuel pump, yank the line off and watch it pump gas to the carb as the next step.