"Gentleman" was a somewhat broader term that encompassed multiple more specific classes and was essentially a term for exclusion, to define who was sufficiently "in" as it were, rather than who they were specifically. Higher level yeomen might occasionally be considered gentleman, but usually weren't. Gentry were in some ways the archetypal gentleman class, composed specifically of all those who's wealth and status, particularly inherited wealth which was more respectable, qualified them as clear gentleman but were not titled aristocrats. Then there is the aristocracy in the various layers and personal standings, and the various species of princedom; kings, emperors, grand dukes, etc. High-ranking clergy like bishops and especially archbishops and cardinals would be considered equivalent to a gentleman, often with similar lifestyle in terms of their wealth, fine living style and land holdings, but wouldn't typically be called a gentleman because of their dubious background; they might come from relatively low.

In your case, this person is probably from the gentry, since aristocrats liked to distinguish themselves as being more than merely gentleman, competing with the gentry in much same the way gentry raised themselves above the other commoners as gentleman. They could have some noble blood in their, and we could certainly see the gentry as coming to be a kind of second set of nobles in this time, but I suspect they were at least mostly gentry. While the son of an aristocrat would not have a title unless they were the heir AND their father had two or more titles, in which case they could use a courtesy title, they would still generally be distinguished as an aristocrat, a distinction they took very serious in this period because the gentry were competing with them so much. Given your ancestor has no known parentage at all in your link, I would surprised if they were the son of anyone with a title, that tended to well-recorded and boasted of. They were probably more of a local squire or merchant family, is my guess.

The most crucial part of a gentleman lifestyle is that they typically had an estate to run. Indeed, it might be considered a condition of being a gentleman to have at least a small estate with a tenant or two. Families seeking to become gentlemen acquired landed estates and families who could pass those down through the generations would be well established as gentry. So they would have at least an indirect role, through their discussion with their servants and other agents, in collecting rents, managing assets like hunting woods and rivers, and in exercising control over their tenants. Traditionally, estate-owners held manorial courts, which some have suggested declined in this period but Brodie Waddell in "Governing England Through the Manor Courts- 1550-1850" suggests their significant was not last as soon or as quickly as you might think. They suggest the biggest piece of business that came before these courts was local infrastructure, which makes sense since it was not uncommon for landowners to own and raise money from public utilities, such as communal bread ovens and mills, it was naturally their responsibility. Landowning gentlemen might also occupy a local political office in recognition and reinforcement of their land-owning status, something like a sheriff, county treasurer, lord lieutenant (militia leader), or justice of the peace. This would further their ability to control tenants and raise their status. Landowners might also except to either be elected in the House of Commons, which was really dominated by the gentry and not what we would think of as "common people", to have their sons or other male relatives elected, or generally influence the elections in their area. And they were often military officers or some rank or another when armies were mustered.

Furthermore, both aristocrats and gentry had considerable social expectations on them. They were expected to spend a lot and show off, debt was quite common, and they would be expected to interact regularly with their neighbours of equal or above rank, including visiting, hosting visits, and attending and host larger parties. Various relatives might stay with them or visit them, even if they weren't close at all because kinship networks tended to taken very seriously. They might also be encouraged to show their generous side with charitable contributions, or crucially, through patronage.

It cannot be overstated how important networks of patronage and favour were in historical Europe. If you were a gentleman, you might have relatives expecting a favour, servants hoping for a good word in their other endeavours or when transferring, artists and scholars you know might ask for commission or other career support, neighbours, friends, anyone really. If you had patronage to give people wanted it, and it was your job to sort out who deserved it. That might involve them doing a favour for you or paying you, or it might via their status as relatives, or a longer period of general service. In a world where your birth could determine your worth, who you knew in your lifetime was equally important. For title-less gentry, they themselves might pursue aristocrats hoping for some of that high-borness to rub off on them, for example the Howards inherited the dukedom of Norfolk from the Mowbray family by marrying a lot of aristocrats' daughters. Obviously, if you are gentry you might not be able to expect their firstborn or favourite daughter, but you might get one of their spare daughters. That probably won't get you titles unless you get lucky, but it doesn't hurt your standing, especially since it can seal alliances with those families and tie them to your personal cause.

And of course, such people had time for hobbies; reading, writing (academic or poetic), sports (including tennis and bowls), hunting, chess, checkers, gambling, you name it. Henry Percy 9th Early of Northumberland in the early 17th century was known as "the Wizard Earl" for his famous interest in a mixture of science and occult matters, under an alchemical sort of umbrella. Henry VIII, Elizabeth I and James VI and I all hunted and rode regularly (particularly James who was obsessed with these activities) and all dabbled in writing poems (Henry VIII also wrote tunes). Henry sometimes played dress-up in his younger years. Elizabeth I played the lute and the virginals, and she also loved to listen to music and to dance. James VI and I also wrote academic works on political philosophy and religion (see Basilikon Doron and Daemology), he was also a massive drinker.

So while gentleman could often afford to be a little idle if they wished, they were far from lacking in things to do, even to extent of having responsibilities and obligations. It would depend on their exact rank though, and upon their character in what they choose to do with themselves.