Hi,
The bad news (as you probably already have a firm grasp of) is that is some very "Slim Pickins" (remember him from the movie Dr.Strangelove?) as far as info goes.
The GOOD news is that Honda twin cylinder outboards, for the most part, remain consistently the same over several years within a "series break" or "model upgrade" period.
As a result, you typically won't need to identify the exact year to get "close enough" to get the parts you may need in many instances. Not all but many.
The 15hp models came in two "basic" iterations ie: earlier A models and later D models.
Broadly stated, the A model was from pre 1997 up to 2002
The D model was introduced in 2003 and is still sold AFAIK. I haven't seen any of them later than around 2014 but that's because I'm old not because they're out of production.
The two models look very different from one another and can be loosely identified by the oil case and engine hood.
What brand and number are the spark plugs your outboard has now?
I typed BAAE into boats.net search and it spit out NGK DR6HS plugs.
Those plugs were specified for most.A model 15hp engines.
If they're Denso (yuck), the number would be X20FRSU for the A model engines.
Sadly, many of the parts for the A model 15hp can no longer be purchased new. But things like waterpump kits and fuel pump diaphragms are still available for the 02 models.
More GOOD news about ALL of these Honda twin outboards is that there were GOBS of them sold and many are still around. The "bad" news is that they are VERY rugged, reliable and popular so finding a not running parts donor outboard might be difficult.
I know this isn't the precise information that you're looking for but it should give you a bit of hope that you can get your "new to you" outboard going and keep it going.
Glad to try helping looking up parts so don't hesitate to ask.
Good luck and keep us updated on your journey.