Is using "wish" like this exclusive to India? “Did you wish her?”
Solution 1:
I have a hunch that the InEng (IE/IndE) usage is derived from the polite valediction, Best wishes, i.e. “I hope everything goes well for you”, and the phrase “send her/him my best wishes”. In both expressions two objects are not required, it is understood that the speaker is saying ‘I would like to send you the best of luck today.’
The InEng usage of ‘wishes’(noun) sounds almost Italian to my ears. In Italian the expression is auguri, and it's very common to just say to one another Auguri! when it is Christmas or the New Year. Tanti auguri is literally ‘many wishes’ which Italians say to each other on birthdays, it is also used to say ‘congratulations’ and ‘good luck’.
But do BrEng speakers use this form? No, not really. Before joining El&U two years ago, I had never heard this form of exchange before; e.g. “Did you wish mum?” In none of the English coursebooks or grammar books I have bought over the years, have I come across this usage, so my guess would be that it is currently considered non-standard English. But whether native speakers would understand it, is a different question, and I'd say ‘absolutely!’
In "I wish my colleague", there's nothing to decypher. Context will tell us if, for example, the colleague is retiring or on maternity leave.
The form has also entered the dictionary. In Cambridge Dictionaries Online
wish verb (GREET)
[Transitive] Indian English to welcome someone with particular words or a particular action: He wishes me every morning.
And its usage has been recorded by linguists and experts
Register Variation in Indian English
By Chandrika BalasubramanianIndeed, Nihilani et al identify 1000 items (many lexical) in their lexicon of usage which they claim are “are used in a distinctive manner by large numbers of educated Indian speakers of English”
Wish: “IVE (Indian Vernacular English) speakers often use this verb where a BS speaker would say ‘greet’. In BS (British Standard), what is wished must be expressed...”
- He wished me when we met this morning.
- He's stopped wishing me
How might a native speaker say the following sentence in British English?
Ever since we broke up she doesn't even wish me on birthdays.
- Since we've broken up, she doesn't even call me on my birthday
- She never calls. She doesn't even wish me ‘Happy Birthday’ since we split up
Solution 2:
Do native speakers use wish like this?
I haven't heard this use before (British English). The way you are using wish - preferring not to specify the wished-for thing - sounds very like the way I would use the word 'bless' (which I don't use often).
Does this sound right to them?
It's unfamiliar but not off-puttingly so, and certainly thought-provoking!
This is how I would phrase the example sentences?
It's her birthday today. Did you wish her? It's her birthday today. Did you wish her 'Happy birthday'?
Ever since we broke up she doesn't even wish me on birthdays. Ever since we broke up she hasn't even remembered my birthday.