And where were you running it when you noticed this? IF it was in a tank or on muffs, it may not "pee" much at idle, mine doen't, even with a rebuilt water pump and new impeller.
Even so, if your impeller is over a year old, you need a new one.
Yes, you'll have to pull your lower unit and check/replace your impeller. I'll bet the impeller is half gone or more. Do not run it until you find out the cause, Head and cylinder damage can happen pretty quickly if you're running hot. The cooling systems on these are pretty simple, and doing it yourself will let you understand how the whole system works. Easy job.
The first thing to check is the pee line itself. It could be clogged (partially). This same thing happened to my engine. There was some debris lodge at the pee orifice. I took a small piece of wire and cleared it.
I kinda sorta have the same problem. When I first start the motor, it takes a minute or so before the engine starts peeing. If I give it a lil gas, it starts and pee's just fine. Under way it also pee's fine. I'm changing the impeller anyway, so I didn't put much worry into it. Thinking about spending the extra $$$ and going with neoprene instead of rubber.