All that can presently (August 2021) be gleaned about Rose Sylvester from sheet music covers and by Internet searching is that she has been featured on 3 works published between 1894 and 1899.
Of interest is Mister Man (1894) music by T. Vincent Davies, words by Hilda Hunter and published by Francis, Day & Hunter, London W.C.2, England. It's front cover colourfully illustrates the good lady.
The Welsh Evening Express of 13th November 1895 prints a salacious article entitled A Newington Man's Wife HOW AND WHY SHE LEFT HIM FOR ANOTHER. Therein, Rose Sylvester was named as co-respondent and described as a "little music-hall girl" aged about 18. The article also informs that she was at the Alhambra Music-hall. Brighton in February 1895, later at the South London Music Hall and then travelled to Johannesburg, South Africa.
Surfers are welcome to contribute any further information about this performer.