Photographs depicting staff working the Inchture Tramway are only available from relatively late in its life, namely, the Edwardian era. These show that both drivers and conductors wore robust but informal attire, comprising hard-wearing jackets and trousers, along with the working man's headgear of choice at this time, the flat cap.
Given that the tramway was owned by a railway company, it is perhaps somewhat surprising that crews did not wear uniforms or carry insignia of any kind. Whether any of the companies which owned the line in the 19th Century (The Dundee and Perth Railway, 1848-1863; The Scottish Central Railway, 1863-1865: or the Caledonian Railway, 1865 onwards) is currently impossible to say, though it remains a possibility.
For a brief history of the Inchture Tramway, see 'Tramways of the Tay Valley' by Alan W Brotchie (Dundee Museum and Art Gallery; 1965).
Horse tram drivers and conductors
The Inchture tram (know locally as the 'bus') at Crossgates circa 1905.
A blow-up of the above photo showing the driver - Bob Speed - who apparently drove the tramcar (and its predecessor - a coach) from the opening of the branch through to 1907, when his son took over. He is wearing informal attire.
Another blow-up of the above photo showing the conductor, whose only badge of office is his cash bag.
Crossgates once again, this time with Bob Speed's son at the helm - 1909.
A blow-up of the above photo showing the driver, who is once again in completely informal attire.