Don't sweat about not finding it, it's more than likely long gone anyway.
If it's not in the hose, and not in the heat exchanger, and not in the hose to the mixing elbow, then it's not going to cause you any problems. One of those jammed in a hose could definitely cause problems, though, so it is in your best interests to spend an hour and a half checking those three things for it. If it's not there, shrug and move on with the pump replacement.
great post Beej and getting a kind word in addition to experienced hel is great.
I find kind words go a long way to reinforcing your confidence when working on sailboats. First (and only, thank god) time I broke my muffler, I was troubleshooting my exhaust system in much the same way as we're talking about in this thread. I cursed, screamed, yelled, and made a general ass of myself in my marina, ended up asking an Old Codger down the way for advice. He and his wife were both in their 80s, had given up their sailboat in favor of a Maine lobsterboat, converted for light coastal cruising, since it was flat, slow, and easy to get around in for old folks. He went on to tell me how he'd broken at least 3 mufflers in his day, and not to worry about it so much.
Good advice on the hose, since one piece was in the host chances are the other one is too, there is a ziptie or two guiding it so I'll make sure I mark those locations... is this hose of a specific type ? it seemed to have a cover that was somewhat different, like a paint on it.... I'll call the local yanmar guys tomorrow they are great for small parts.
If I recall correctly, the "original" hose that connects the raw water pump to the heat exchanger on a Yanmar is pre-bent, to follow the contours of the engine and whatnot, and is painted the same color as the engine. If you can get a replacement from Yanmar that'll work fine, but I just used a length of radiator hose when I replaced mine. It bends out away from the engine kinda funny, so I ziptied it away from the belts so they don't rub. These are the concessions you make when you're doing maintenance an hour drive from the nearest marine parts store, and when your local Yanmar dealer is such a bunch of losers they can't even order you a radiator cap without screwing it up.
oh also, how long can I run the engine while debugging the raw water problem ? I'm thinking the impellers probably need water as well as the engine not over heating, just trying to figure how much time I have to test the new setup.
Watch your overheat light, your engine's good until it starts to glow, as far as I'm aware. For the impellers, don't sweat running them dry a little bit starting up. It'll usually take your engine ten, maybe twenty seconds to get the raw water all the way through the system, so monitor your exhaust for water. Also, I check my tailpipe every time I start the engine, out of habit, and I highly suggest you pick that habit up as well, it's the first easy check whether your raw water system is working. Once you get a feel for how much water should be coming out of your tailpipe, you can infer when you've got a problem before it gets too bad.
DO NOT FORGET to open your seacock! That's got to be the #1 source of "whoops" error when troubleshooting a raw water pump. I heard one guy say (maybe on here) that he ties his engine key on a string, and hangs it on his thru hull valve whenever he shuts it, to remind him not to start the engine without opening the thru hull.
Another note - this is something I only recently found out about - mixing elbow lifespan is supposedly only 8 or 9 years, and should be replaced as part of general maintenance. In addition, idling Yanmars is supposedly bad for them, because it causes carbon buildup in the exhaust system. I never knew that until recently. I've got a carbon problem in my current mixing elbow, and have to replace the whole shebang next time I'm down. Probably could have eeked out another year or four of service life from the part if I didn't idle the engine.