I can't remember how far back the Minehead buses have diverted via Station Road in Taunton, it's been a long time and I think may pre-date the closure of the BR Minehead line in 1971, in that certain services at least, such as winter Sundays when the branch was closed, did used to do it. I also think that at the time rail return tickets were "interavailable" to use on the bus.
However, only Minehead did it. The parallel service to Wiveliscombe did not, even after the closure of the Barnstaple branch. This used to carry just as many passengers out of Taunton. The greatest value would be the one to Wellington, the largest town around with no station.
Alas my old Western National timetables from those far-off days are long gone. I do remember the Minehead bus timetable long indicated that if the last bus of the day, about 2230, got to the cinema at the start of Station Road before the last film of the evening had finished, it would wait until everyone had come out - I bet that doesn't happen any more.