OK was originally a separate thing that used to occur in locations other than between the two words. I distinctly recall this from my childhood. Don't know the origins of it but there is some suggestion on the internet that it was copied from Tata trucks which had the logo of the OK soap (a lotus).

They could occur in the current order, but it was not necessary. It should still be read as separate from the "horn please" phrase.

As the country became functionally more illiterate over the years (yes, probably a controversial opinion :) ), the three words were just rote copied inline and painted on trucks, with the meaning lost to time.

During WW2, due to fuel shortages, Indian trucks often switched to Kerosene.

OK means: "On Kerosene". OK was painted on the back of trucks and other vehicles to warn other drivers to maintain a safe distance because Kerosene is highly flammable.

Due to another meaning of OK, they just kept doing it. [0]

[0]: https://www.fr8.in/blog/why-is-horn-ok-please-written-behind...

I was told that this was the polite honk triplet - the two honk call and one honk response.

"honk honk" / "honk"

"horn ok" / "please"