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.

This list is derived from information provided by Monologues.co.uk which went down sometime in 2023.
The loss of this valuable resource is very sad and a mystery.