I don't know how excited you might be about buying more parts and doing more work but the link below shows the requisite items to access for the "full Monty" cooling system flush.
With items 8 (thermostat) and 12 removed, you can really get after it and backflush (there's that word again!) the system.
Although, you would want to have the gear case off so that anything beIng pushed out, the way it came in, has the easiest path to exit.
You would need a new water jacket cover seal, item 13 along with a new thermostat cover gasket, item 11
But I also recommend a new thermostat along with a new sacrificial anode zinc with mounting screw items 4 and 30 while you're in there.
Then there's item 9, the tell tale fitting that screws into the block and the tell tale hose/hose, item 29. The tube should be soft and supple to allow small pieces of debris to pass. They harden over time and have a tendency to catch things rather than letting them through.
The tube connects to item 35, the "water check grommet" or, simply, the fitting in the link below.
Now, doing all that now may be a big ask at this time when, in fact, you may just need to clear the tell tale bypass passage behind the fitting screwed into the block to get the pee stream back.
But I advocate doing this on a "new to you" outboard of this vintage because...
1. It's probably never Ben done
2. It could save you heartache later.
The hardware associated with outboard cooling systems tend to sieze when left undisturbed fir a long time. That little zinc needs to be fresh to help protect the other metals.
Around 70% of all catastrophic engine failures originate in poorly working cooling systems.
Do you have any knowledge about when the last waterpump service was done?
See! I told you I was ENTHUSIASTIC!
But, then, I'm not the one doing the work or spending the bucks!
Just some thoughts.