Hello Wendy
I cannot find a link to the Cheshire regiment reference your Thomas Fullerton who served in the SALH. His attestation papers record him as being single in 1901 and aged 25. He was of Irish decent and there are certainly quite a few Fullertons who served in Irish regiments. Alas, no Cheshire connection. Do you have any details pertaining to the Cheshire regiment and your Great Grandmother beside the letters?
Could there be another surname that may have been used?
India is certainly prominent regarding Norah, as she served in the Queen Alexandra's Military Nursing Service for India during WW1. With reference to the Cheshire Regiment and service in India, both Battalions served in Burma between 1887 and 1891 and the 2nd Battalion saw active service in South Africa from 1900 to 1902. However, the above dates for India / Burma would put your SALH Thomas Fullerton at aged 12 and 15. The Cheshire regiment also served in India during 1843 but I think this information is irrelevant regarding your quest.
I will keep searching, but at present I believe that your original Thomas Fullerton who died in January 1902 may not be the father of your Great Grandmother. The enigma remains, who was the gentleman who served with the Cheshire's or indeed another regiment who may have fathered Evelyn and Norah? I didn't have much luck with Evelyn or Norah regarding birth certificates or potential fathers. There are a few records of transportation of Norah working as a Missionary and the nursing information. I did think there may be a link to India / Pakistan with a Lieutenant Colonel J C Fullerton who was a administrative medical officer but that in my opinion maybe a much longer shot, although, it may be worth checking out reference the medical path Evelyn and Norah chose.One last Fullerton I found was a Captain J D Fullerton in the Royal Engineers who served in Burma in 1885 to 1887. Sorry I couldn't be more helpful with your quest. Perhaps a fellow forummer may be able to unravel the mystery.
I wish you well in your future research.
Best wishes
Dave.
A possible lead to a Fullerton and Quetta perhaps.
The Royal Engineers Fullerton
You only live once, but if you do it right, once is enough.
Best regards,
Dave