Although your watch is signed for J. Harrison like the one originally posted in this rather ancient thread, yours is not a "Swiss fake", but an English watch, made in Liverpool as signed, although not the John Harrison of Longitude fame; there are other watches known signed for this Harrison, and there's no reason to suppose that he didn't exist!
It looks like a decent quality watch with a fancy gold dial in an ornate gold case, dating from sometime in the second quarter of the 19th century. If you can take some pictures of any stamped marks inside the case we can probably date it more accurately and tell who made the case, if they're English hallmarks.
I suggest that we ask a Moderator to split this post off and start a new thread for you.
I've already asked if it can be split off. The small triangle icon at the bottom of each post is used to talk to a Moderator.
Your pictures confirm that the case isn't English, but as Keith has said, American, which is not unusual to find, since many bare movements were exported from Liverpool and cased in the US to get around import duties. Unfortunately, there isn't the dating information here which English hallmarks would provide, but someone may know about the case maker's activity.
If you do decide to have the case tested, please don't use acid; it only confirms the surface composition and disfigures the case needlessly. There are non-destructive ways of doing this. In any case, knowing whether it's 14 or 18 carat, or indeed anything else, in my opinion has little relevance to the aesthetic or technical merits of a watch.