The vast majority of the surviving Scottish birth/baptism, banns/marriages and deaths (but not burials) are online at
www.scotlandspeople.gov.uk.
Not sure why you think "the Presbyterian records are not available online", because they are.
The term presbyterian describes a system of church hierarchy, not a set of beliefs or doctrines. The Church of Scotland is presbyterian, and so are most of the breakaway denominations in Scotland.
It means that instead of a pyramid of clergy culminating in bishops and archbishops, a presbyterian denomination is organised in tiers of committees.
The bottom tier is the kirk session, which is the committee of ministers and elders that runs the affairs of an individual kirk or parish.
The next tier is the presbytery, which is a committee made up of the ministers and one representative elder from each kirk session in the presbytery's geographical area. Above the presbyteries are larger committees called synods, covering several presbyteries, and the top tier is the general assembly.
Scotland's People has all but a tiny handful of the surviving records of Church of Scotland parishes, and the bulk of the surviving records held by the National Records of Scotland of other denominations. These have been digitised and are available online. They are pay-per-view but modestly priced.
Northumberland is a historic county, the most northerly in England, including the city of Newcastle-upon-Tyne and the town of Berwick-upon-Tweed. In practical terms the records you are likely to want will be from Northumberland. See
https://en.wikipedia.org/wiki/Northumberland and
https://www.genuki.org.uk/big/eng/NBLNorthumbria has two meanings. It can mean either an ancient kingdom that pre-dates the historic counties, and it is also the name given to a modern local government area that replaced Northumberland in the latter part of the 20th century.
https://en.wikipedia.org/wiki/Northumbria_(disambiguation)
Realistically, you are not going to be able to home in on John Gibson, born 1807, without more information. For instance, did he marry Elizabeth Miller in Scotland? If so, there appear to be three records of interest. One in 1831 in Edrom, which is in Berwickshire, close to the English border, and one each in 1832 in Bervie and Arbuthnott. These parishes are close to one another in Kincardineshire so the likelihood is that this is one couple who, before their marriage, lived in different parishes. Their banns would have been proclaimed in both parishes, resulting in a double record of the same event.
One thing to be aware of is that the surviving records are far from comprehensive, so you must never assume that the only candidate who roughly matches your ancestor is necessarily the right one.