Possibly Thomas William Tucker, born Houghton-le-Spring, County Durham, in the fourth quarter of 1875 (mother's maiden name was Routley). I can't find any UK births for T. W. Jensen that match, and neither can I find any other references to T. W. Jensen. However, I've found some for Thomas Tucker, all in the Sunderland Daily Echo: -
24.1.1900 - '"Writing from the Wynberg Hospital, where he is being treated for an injury to the foot, Private Thomas Tucker, of the Black Watch regiment, states: "I know whose blame it was; we got cut up; but we will let that drop for the present. When Major-General Wauchope got shot, the men wanted to carry him off the field, but he resisted. He spoke to them and told them that it was not his fault, and that he had only done what he was told to do. He told the men to lie down, as it was a man-to-man job." The writer praises the hospital arrangements."
3.2.1900 - "Private Thos. Tucker, of the Black Watch, writing home to his parents from Wynberg Hospital, says: - My wound is healing up all right, but I cannot put my foot on the ground yet, and I have to use a pair of crutches. The people in Wynberg made our Christmas day a splendid success, for they gave us everything we asked for, and the Children's Mission at Capetown sent us twelve stamps each and a lot of writing-paper. We had a tea from the Soldiers' Home at Capetown, and enjoyed it "immense." The nurses who look after us here are very kind, and give us plenty of tobacco and fruit. We had three of the mounted infantry wounded through the treachery of the Boers. They were in a farm, and a woman commenced to wave her hands for them to come to the farm, and when they got near they were received with a volley from the windows of the farm. They were all wounded, but two of them managed to escape, whilst the third one was found near the railway (bandaged, it is said, by a woman) when we were out with the armoured train."
11.6.1900 - "On Saturday night in honour of the occupation of Pretoria several additions were made to the performance at the Avenue Theatre. The full band of the 1st D.A.V., under Mr W. W. Lax, played a descriptive piece entitled the "Battle of Waterloo," and Mr Percival Craig recited "Something to Remember," which was received with great enthusiasm. Three local men who had been wounded in South Africa made their appearance on the stage. They were Corporal Noble, of the Coldstream Guards; Private Carty, of the Northumberland Fusiliers; and Private Tucker, of the Black Watch. As each man was introduced by Mr Craig he received quite an ovation from the audience."
22.3.1901 - At the Sunderland Police Court, the same date, a case was heard regarding the manager of the Union Flag beerhouse permitting drunkenness on licenced premises. Among those who gave evidence was "Thomas Tucker, private in the Black Watch, who said he served under Gen. Wauchope at the battle of Magersfontein…"
10.9.1902 - Not known if this is the same Thomas Tucker - "Ethel Robinson and Thomas Tucker pleaded guilty to assaulting.....the barman of the Golden Lion public-house, High Street East....Defendants were fined 5s and costs each."
Was this what happened? - Thomas was born to parents Mr and Mrs Tucker. Mr Tucker later died, and Mrs Tucker re-married, to Mr Jensen. Thomas chose to use his birth-father's surname, but Mr Jensen preferred to call him Thomas Jensen. If that was the case, he wasn't really a Dane, only through his stepfather.