I would have said that 7524 would have been the more likely of the two, a Volunteer in an Active Service Company would lend itself nicely, but, I can't see any available on line folio regarding papers which does not surprise me, it would have been better if they were Militiamen.
There is a note in the case of 7524 on the main roll which says "disembarked Capetown" on the 11th of April 1902.
I'd go with Meurig's suggestion, find the name of the local newspaper of the day and then locate any existing copies, normally available on microfilm at libraries and county record offices, then trawl through it.
What do you think, I can't see him being 5925, the Manchester Regiment raised the 3rd and 4th Battalions for the war and renumbered it's Militia as a result, I would have thought if Wilkinson had served in the war he can only be 7524.
7524 is indeed the James Wilkinson being asked about.
From the Haslingden Gazette, 9th August 1902: -
LATE PRIVATE JAS. WILKINSON. - The Haslingden Volunteers attended service at Haslingden Parish Church on Sunday morning as a tribute of respect to the late Private James Wilkinson, who died from enteric fever at Heilbron, South Africa, on June 25th. The deceased went out for active service with the third detachment sent out by the Haslingden company. While with the Volunteer Company at Haslingden he was a valued member of the band. He was about 23 years old, and leaves a widow and one child. There was a good muster of Volunteers for the parade on Sunday morning, and Capt. Halstead and Lieut. Warburton were present. At the church the vicar, Rev. A. Spencer, preached from the text, "Peace, I leave you; peace I give unto you, not as the world giveth, give I unto you. Let not your heart be troubled, nor let it be afraid. (John xiv., 27). He referred to the service rendered by men who were out on active service from Haslingden, and in speaking of those who had died in South Africa expressed sympathy with the family of the late Pte. Wilkinson. At the conclusion of the service Mr. F. Tattersall, who at this service commenced duties as organist at the church, played the "Dead March," the congregation standing.
James is remembered on the town's memorial inside St. James' Church, Haslingden.