Crossword Genius

Where the cowboy couldn’t stay on a horse? (5)

Ross

I believe the answer is:

rodeo

I'm a little stuck... Click here to teach me more about this clue!

This might be a double definition.

'where the cowboy couldn't stay' is the first definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

'horse?' is the second definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'on a' acts as a link.

Can you help me to learn more?

(Other definitions for rodeo that I've seen before include "Originally, a round up of cattle" , "Cowboys' riding contest" , "Cattle round-up" , "Cowboy event" , "American show" .)

I've seen this clue in the Evening Standard.
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