I jumped to the conclusion it was a London gun... obviously a mistake if its from Dublin (which wasn't mentioned in the original post.) If it is Govers and its a Dublin gun, then my comments are indeed wrong.
As to the mounts...I hadn't seen the top view but I still think they could be as late as the l 70s though I agree they would have been old fashioned by then. I have a primary source reference to Jover as a witness in a trial at the Old Bailey in 1770. This is five years earlier than the entry in Blackmore. I think that the elder Jover was born around 1737. The son, William Jnr, was born in 1762 so he would have been about 22 when he went into partnership with his father in 1784. Its impossible to tell how long William Sr. had been in business but it could certainly be as early as 1765.
Jover almost certainly started earlier than the London directory listings suggest but if most of his work was for the trade, or he had a loyal following, he may not have bothered with directory listing (which often had to be paid for). He probably died around 1801/02 since his wife, Mary, is listed as a gunmaker from 05 to 08. Apparently he wasn't a member of the gunmakers company so there is no apprenticeship record for him. In fact, it looks as if he came from West Bromwich, one of the black country gunmaking towns on the outskirts of Birmingham which would explain the lack of a London apprenticeship record.
I had a good friend who was particularly fond of this maker and had half a dozen of his pistols, including a nice cased pair that could easily be a very early pair of dueling pistols although in form they don't look like conventional duelers. Jover's early guns were very conservative in style which is certainly understandable if he learned the trade in a provincial center and can easily be taken as older than they probably are.
However...please take all this guardedly. Much of it comes from a work-in-progress and I would not be surprised to have to change my findings as new information surfaces.
James... what source are you using for the dates? I am going by Blackmore and other primary documents. I have reservations about some dates in many of the standard sources. I've been doing a little side study on where certain dates that are widely accepted come from and I've found that many have simply been repeated time and again from very early works where the authors simply guessed...for instance, I doubt the William Jover Sr. could be as early as 1750 since he was probably about 13 at the time.