I.e. is there a known historical reason behind why the British began calling each other "governor" and "guv"? The various online dictionaries I've consulted say it is now a way to refer to those of elder status, but I was wondering how it was adopted in the first place. And is it still used frequently amongst native British speakers?
It depends where you go. In some communities it is used a lot, in others not so much.
It is not used for elders at all, not that I've ever noticed. It is used to show deference to either your boss, or a person you are currently serving. It is quite common in East London, among a certain type of people, almost always men, to other men, can't recall ever hearing a woman use it in public, or to a woman, apart from inside the civil forces (it is often used in the police and fire brigade for superiors by subordinates, regardless of sex).
Using it in full, as governor (usually slightly contracted by accent to guv'ner), is not overly common, it sounds odd to my London ear, slightly archaic. If someone used it to someone, I would assume they were being insincere with the respect it implies; the senior prison manager is called a governor usually and the prisoners will use it with contempt.
Guv is used plenty though, plenty of people use boss instead, in the same way. Particularly in immigrant communities. I personally use sir in the same way, as do some more old fashioned people as a form of general politeness. This usage is mainly employed in trade, if I get a taxi, the driver is liable to call me guv, or boss, or sir. I am liable to call him sir.
By no means all people do this, it is just a form of politeness particular to certain situations.
Guv is still used in certain companies and organisations for the manager, or, more likely, foreman. Just a form of address. This is it's original usage in the current form, coming down from Latin via French.
Apologies for the resurrection...
The term 'guv' or 'governor' is most commonly used for a reason by manual tradespeople, to denote the person paying their bill, or the person who orders and accepts their work, to distinguish from the tenant, the property's legal owner, and so on. The governor is the person who they are answerable to. Since manual tradespeople tend to, on average, take a larger than average part in the social lives of their communities, their parlance propagates quite effectively.