Begin with the movement, not the case. Plate shape, pillar form, wheel-cutting, the arrangement of the strike work and the escapement type are the features that carry regional and period information.
Strike systems are strongly diagnostic. Count-wheel striking, rack striking, and the various quarter-striking and chiming arrangements belong to identifiable periods and traditions, and their layouts differ between English, French, German and Austrian practice.
Case and dial then narrow it. Dial material and layout, chapter-ring style, spandrel castings, hood and trunk proportions, veneer and moulding profiles all move a clock within decades once compared against published examples.
Numbers and marks are worth hunting for. Movement and case makers' stamps, assembly numbers scratched inside plates and doors, factory trademarks and paper labels are often present but hidden behind dials, on seatboards or inside backboards.
Write the conclusion as evidence. 'English eight-day rack-striking longcase movement, anchor escapement, case of mid-eighteenth-century form; maker unidentified' is a defensible record; a confident name without a signature or archive entry is not.