I have found the following entry in an 1850 Dundee Directory:
"Henderson William watchmaker and jeweller 32 Nethergate; h. St Mary's close"
I have also found some old photos of 32 Nethergate, Dundee here http://photopolis.dundeecity.gov.uk/wc0479.htm. The text accompanying this photo states:
"James Rattray, the watchmaker and jewellery business founded in 1850, and worked by him George D. Rattray, was No. 32, ..."
There are other photos of 32 Nethergate which are accompanied by the followinbg text:
"James Rattray, the watch and clock maker, jeweller, and gold and silversmith at No. 32, remains on the site in 2000. In 1894, Rattray lived at No. 25 Windsor Street, while George D. Rattray, watchmaker, lived at No. 19 Louise Terrace in Broughty Ferry."
and "James Rattray, the silversmith and jeweller at No. 32 founded in 1850, has survived to the present day (2000). An advertisement in the Dundee Directory of 1896-97 says 'contracts entered into for repairs and alternations of church and turret clocks'."
I wonder whether William Henderson worked for James Rattray or whether the shop changed hands in 1850.
My ancestors were living in Dundee in the mid 1800's so I guess there is a link here but I don't know if the watch was bought secondhand from 32 Nethergate of whether it was repaired there. It has signs of being repaired but that obviously doesn't prove much.
The numbers on the back of the paper interest me. I thought at first that it isn't a date because of the reverse order of month and day (which is called middle endian form and is used now, for example, in the United States). However Wikipedia informs me that "This date format was commonly used alongside the small endian form in the United Kingdom until the early 20th Century"
Therefore the numbers, read from top to bottom could represent 24th October 1837 (possibly 1857).
I will do some more research soon...