Seeing the original records always helps! The places he served are as Jebbers says. The nuisance is that the units he served in are not immediately distinguishable but looking at the entirety of the record we find:
Jan 1903 signs on for a 12 year engagement consisting of 3 years active service followed by 9 years reserve service. He is a mason and later documents show his testing at increasing levels of skill in that trade.
In March 1904 he is in Ireland with 54 Company and changes his engagement to 8 years with the colours.
In 1906 he is promoted Lance Corporal but reverts to Sapper in 1907 losing his good conduct badge on the way.
In 1909 what you saw as 58 Company 12 Battalion is not that, the RE were organised in companies not battalions (with a minor exception or two). He is transferred from 58 Company to 12 Company
In 1911 he has now finished the eight years he signed up for and is transferred to the reserve.
In 1914 he is still on the reserve so when war breaks out he is recalled on 8 August and goes to France on 17 August 1914 with 11 Field Company.
His commitment ends in 1916 and he is discharged Jan 1916.
As far as finding out what he was doing, the war diaries for the period he was in France in 1914/16 are at the National Archives
http://discovery.nationalarchives.gov.uk/results/r?_aq=engineers&_ep=11%20Field%20Company&_nq1=australian&_nq2=canadian&_cr=WO%2095&_dss=range&_ro=any&_st=advWe can't be sure that prior to the transfer from 58 Company in 1909 that that was the only company he served in after 54 Company in Ireland but it at least gives something to start with.
The period in Africa is more difficult and my feeling is that you will need the museum for that. There were a number of expeditions to Africa in the time frame, not major wars so history may have almost overlooked them.
That's a first quick look.
MaxD