2.3's were put out from 1996 thru 1999. Good News, it's a lot newer than you thought!
Anyway, you'll have to go by model # to find the correct diagram for yours, but to start with here's the 2.3's for 1996:
www.marineengine.com/parts/johnson-evinrude-parts.php?year=1996&hp=2.3
On the float, looks like it slides on the main jet/needle post. I'd imagine that, with the float bowl off, if you were to put together the float assembly with the carb upside down, screwing the main jet/needle assy into the carb, you can get an approximation of float level. Obviously it's impossible to adjust once you put the float bowl on. Not the greatest design, eh!
I've worked on some of these "Weedwacker" outboards with carbs that have impossibly small passages.
Best you can do is juice the heck out of it with carb spray, then give it a vigorous shot of air with a blow nozzle. Any little speck of debris lodged in there can cause issues.
BTW these take so very little fuel that you can easily flood them if anything is out of adjustment. If you suspect flooding, remove fuel and see what happens.
I didn't even notice before, but this is a slide valve carb like a Japanese motorcycle. Maybe it's a Keihin carb?? Or a copy of.
At any rate, it has a mixture needle that goes down thru the slide, and as the slide raises, the tapered needle lets more and more fuel thru.
Note there's a teeny weeny E-clip that goes into a groove on the needle. Looks like there are a number of grooves, for adjustment. This is just like as used on a motorcycle. If you lower the needle in the slide, it's gonna run leaner. If you raise the needle it'll run richer. So they are tuneable to some extent.
If it's been fiddled with, it might not run at all. So check all the settings and adjustments.
Boats.net also has listings for these, and good parts diagrams to go with:
www.boats.net/catalog/johnson/outboard/2-3hp
At least you'll be able to pin down the year of yours, and it should be a lot easier to find a manual now that you know the correct production years.
HTH & G'luck............ed