What makes a Turkish March, a Turkish March?

I am composing a Turkish March but this is one of very few times where the type of piece I am composing is so rare that I can only find a few examples of it.

In fact, I can only find 2 just by searching on Youtube(I bet there are more on IMSLP but I haven't looked there yet). There is the one in Bb by Beethoven. And then there is the infamous Rondo Alla Turka by Mozart.

This is all I can get on Wikipedia on what a Turkish March is:

A march composed in the Turkish style.

Yeah, that isn't very helpful when I don't know what the Turkish style is specifically.

And these are the conclusions that I can draw just by listening to the 2 Turkish Marches I can find:

• Basic pulse of 8th notes at quarter note=110 BPM
• Movement in the left hand that sounds sort of like a chord in footsteps
• Major key with minor key added for harmony(which seems to be the case with Beethoven) or drama(the case for Mozart)
• Overall upbeat feeling except in minor key sections(such as the F# minor sections of Rondo Alla Turka)
• Rondo form

That is very little compared to say how much I can draw from a dramatic symphony about why it sounds dramatic.

So I don't have much to go on except those 2 pieces as to how to compose a Turkish March(And in both cases, the Turkish March is part of a multi-movement work). I am composing one in C major, which I usually avoid as a composer(C major just feels so uncreative, like if I take a note 1 semitone away from the scale, eveybody will be like "Is this a key change or just an embellishment?" and me wanting to avoid that questioning when possible. If I add Ab to a Bb major piece, it isn't like everybody immediately thinks "You are changing to Eb major/C minor". But with C major, I feel like that is exactly what happens. 1 Eb and it immediately is speculated to change to C minor. 1 Bb and it immediately is speculated to change to F major and so on. So I tend to avoid this key, because it really feels like unless I am modulating, I have to stay within the major scale.

But when I am composing something like a Turkish March for the first time, I often start with C major as like a proof I can compose that type of piece and afterwards compose more in other keys. But still, like less than 1 in 10 of my pieces are in C major. I bet even less than 1 in 100 of my pieces will ever be in C major. But yeah, besides what I have concluded from listening to the 2 Turkish Marches I can find, is there anything else that makes it a Turkish March and not some other type of march?