Ladies 18CT gold Rolex how old

[normaneldon]

Hello I have a vintage ladies demi hunter wrist watch.
It is stem wound pin set.it has an enamel outer chapter on the outer upper case.
The case is signed Rolex
The sponsor hallmark initials look like EH
The case is numbered 586841
The hallmark date looks like 1913/14 but it could be 1953/54 because the date letters are similar.
The diameter of the case is a little over 23 mm
It has an enamel dial.
I would like to know the age of the watch
The movement is signed Rolex 15 jewels
It has swivel lugs
I would like to verify the date looking at the style of the watch I would think the the date would be 1913/14 but searching shows the name Rolex signed cases and movements only appeared in 1915.
I know the ladies watches are of no great value but there is some sentimental value
I would really like the input from the experts on the forum