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"Anything that is "irreducibly complex" is that which is made up of multiple parts, and its function cannot take place if any of those parts is missing." --- How is my definition inadaequate?

It's not a matter of something of multiple parts but of multi parts that can't be simplified without destroying its function. A car has multiple parts but you can remove the trunk lid or radio and it will function. An irreducible car would be the motor, driveshaft, axles, wheels and fuel source.

Without either the propeller, shaft or motor, the flagellum won't function.

Why should it have to?

Why should the TTSS come after the flagellum? It's standard evolutionary theory. Evolutionary biologist think the flagellum has been around for 2-3 billion years. The TTSS is a delivery system for pathogens to multi-celled life which, according to evo biologist have been around for just 600 million years. You're not suggesting that TTSS popped up without a purpose, evolved into the flagellum, then found its role?

I still can't think of even one example that would fit IC.

Taking parts away and saying the function is gone is nonsense.

Example: car

Function: take me from here to there.

Yes, the aimed purpose of a car is gone if you take the motor out. But it will still able rolling down a hill (soapbox). So there is still a function. But not your aimed. Take the tyres away and you'll have something you can make heat. IC?

The function is introduced by an observer. The theory of evolution works with no aim. So even parts with no use are in the game.

For IC you take a function as a basis. But the function or aim is introduced by an observer.

How can we be sure about the function or aim of a flagellum? We just observe the results.

I'd be interested in where you get your dates for TTSS.
Dates on soft parts that don't fossilize are difficult to establish or verify.

Another TTSS paper.
http://www.millerandlevine.com/km/evol/design2/article.html