I’m descended from one of those Hessian soldiers, my earliest ancestor in America. By the family account, he was considered a mercenary. But he did indeed choose to stay in America (New Jersey). It would be interesting to do more research on him, since I only have bare-bones accounts, I’m not clear on his last name.
While the Grenadiers and the German officers were--for the most part--professionals, the average infantryman was a farm boy (not a Pharmboy).
They were in service to the local prince who paid them a yearly stipend and went wherever he sent them, but were not career soldiers by any stretch.
The records kept by the Brits, the Germans and even the Americans at the time were pretty good, and you should--with a modest amount of research--find out a fair amount about your ancestor. Many of the Germans kept diaries and some have been translated, but most still remain in German.
The Germans got a bad name here, partly because of the language problem. The English officers and German officers communicated with each other mostly in French since that was the likely language both groups had in common.
As an example, NJ was constantly patrolled by both sides...and when a Hessian patrol came upon an farmhouse that was actually a Loyalist household, it was bad news for the Loyalist. While they had a certificate from the Crown that protected them from the Redcoats, the Germans could not read it and took their provisions anyway.