I have a Briggs flathead 5hp on a Tiller that will burn your eyes with a nasty unburned fuel smell... ...it absolutely makes your eyes and sinuses burn from all the lean partial misfiring.
I've harped on misfire, but you bring up a valid point. Incomplete combustion of various sorts. It's still "misfire" but "misfire" is kind of a sliding scale from light, to mild, to total.
"Rich smell" and "eye burning fumes" are all a result of hydrocarbon emissions. It's the hot gasoline vapor coming off the tailpipe--or worse, out of the exhaust system rust-holes--that causes the eye-watering and "rich smell".
It doesn't matter if the fuel mixture ratio is too rich to burn properly, or too lean to burn properly. ANYTHING--too rich, too lean, lack of compression, lack of, or improperly-timed spark, etc., that causes outright misfire, or incomplete combustion, provides that "rich smell" to the proportion of fuel not burned completely.
"Gasoline" is essentially hydrogen + carbon = hydrocarbon. When it's fuel for an engine, it's called hydrocarbon. When it's fuel for our bodies, it's a yummy carbohydrate. Go figure.
The hydrogen (H)
readily combines with oxygen (O2) in the air to produce water vapor--H2O. The carbon (C) combines with oxygen in the air to produce Carbon Monoxide (CO). It has to combine with MORE oxygen to reduce to Carbon Dioxide (CO2). So the first thing that happens with a rich mixture is the CO goes out-of-sight because there's not enough oxygen to convert CO to CO2. Even in ancient times (1960s) "Tune-Up" shops had a CO sniffer to determine idle rich-lean. When the idle CO was within limits, the idle mixture screws were assumed to be reasonably correct.
Misfire (or partial misfire) means that some or all of the hydrogen doesn't get a chance to split from the carbon in the hydrocarbon fuel. The raw hydrocarbon blows out the tailpipe (or rust holes) and produces that eye-watering fume.
OK, there's more to fuel-burning and emission testing than (evil) HC, CO, and (not-evil but politically-incorrect) water vapor, and CO2. Vehicles now monitor O2 in the exhaust to determine rich-lean; and we haven't touched on the nitrogen (N) (80% of air) combining with various amounts of oxygen at high temperature to produce NOx.
A FUNCTIONING catalytic converter "converts"
small amounts of HC and CO to their non-poisonous forms--water vapor, and CO2. Too much HC in the exhaust stream will overheat or poison the converter, and then even the little bit of HC from a normal-running engine will smell "rich" to folks now. (Sixty years ago, it was so normal and common that no-one noticed.)
Fancy catalytic converter will also help remove NOx from the exhaust, but not all vehicles are equipped with that sort of catalyst.
