Glasgow Tramways and Omnibus Company Limited
Photos of GT&OCoLtd staff indicate that conductors were issued with single-breasted, calf-length coats, with five buttons (almost certainly brass and bearing the GT&OCoLtd monogram - see link) and lapels. Caps were in the kepi style, and appear not to have carried a cap badge; certainly, none can be seen in photos, and none have ever come to light.
In common with many UK horse tramway operators, drivers were left to decide on their own attire, often turning out in heavy-duty jackets with bowler hats (the headwear of choice for most horse bus and tram drivers during this era). Both drivers and conductors wore a round municipal licence, usually hung from a button or cashbag strap; drivers' licences were black on white enamel, whilst those issued to conductors were black on yellow enamel (see below).
For a detailed history of the GT&OCoLtd, see: 'The Glasgow Horse Tramways' by Struan Jno T Robertson; Scottish Tramway and Transport Society (2000).
Horse tram drivers and conductors
GT&OCoLtd Horsecar No 439 - photo undated, but probably taken in the 1880s. Photo courtesy of the Tramways and Light Railway Society, with thanks to David Voice.
A blow-up of the above photo showing the driver, who is in informal attire, and the conductor, who is wearing a single-breasted uniform jacket with licence and kepi-style cap.
Driver licences, 1st and 2nd Class - white enamel with black lettering.
Conductor licence - yellow enamel with black lettering.
A rather decrepit Horsecar No 380, with crew, taken in 1888. Photo courtesy of the Tramways and Light Railway Society, with thanks to David Voice.
A blow-up of the above photograph showing the conductor, again in single-breasted jacket with kepi-style cap (nonchalantly worn to one side) and with licence hanging from a coat button. Although the photograph is of poor quality, it does seem to suggest that the kepi-style caps did not carry a badge of any kind.
GT&OCoLTd Horsecar No 254 at Finnieston Cross - photo undated, but probably taken in the 1880s. Photo courtesy of the Tramways and Light Railway Society, with thanks to David Voice.
A blow-up of the above photo showing the driver, who is clearly wearing informal but smart attire, along with a bowler hat and a municipal licence.