Apparently the Aleutian Islands campaign was deemed not overseas service by Revenue Canada, and thus troops were ineligible for tax exemption.
There was a tax case heard in the Exchequer Court of Canada in 1947 that refers (somewhat) to this, but does describe how Canadian soldiers, sailors and airmen were subject to income tax during the war.
https://www.canlii.org/en/ca/exch/doc/1947/1947canlii623/1947canlii623.html
It doesn't state explicitly that the individual served in the Aleutians, just that he was not in Canada but still in the Western Hemisphere, so it could have been Newfoundland (one of the major locations where Canadians served outside Canada but still in the Western Hemisphere) or elsewhere. The appellant in this case was a solicitor and served as his own counsel in the matter. Probably a tax lawyer before the war.
Justice O'Connor wrote:
Under the Act, in my opinion, there are four groups of members of the Canadian Naval, Military and Air Forces.
(1) The income, including service pay and allowances of those members of the Forces in Canada who are not in the Canadian Active Service, is subject to taxation.
(2) The income, including service pay and allowances of those members in the Canadian Active Service who are in Canada, is subject to taxation, but under Rule 2 the tax they pay is "reduced by a credit from the tax otherwise payable", ranging from "an amount equal to the tax payable on $1,600" of pay and allowances, on up.
(3) Under Rule 3 the income, including pay and allowances of all members of the Forces in the Western Hemisphere other than in Canada, is subject to taxation because they, under Rule 3, "shall be dealt with in the same manner as the persons referred to in Rule 2 of this section". And the persons under Rule 2 are given "a credit from the tax otherwise payable". They are then subject to the general taxation provision and receive a credit on their tax, depending on the amount of their pay and allowances as provided in Rule 2. But there is one exception under which they get additional relief. That is, that they "shall in respect of his service pay and allowances be subject to tax at one-half of the effective rate of tax applicable to his total income".
(4) Under Section 4(t) (i) the service pay and allowances of members of the Forces while in the Canadian Active Service Forces and Overseas on the strength of an Overseas Unit outside of the Western Hemisphere and certain others described in subsections (ii) and (iii) is not liable to taxation at all. Their income other than pay and allowances is taxable. A member of the Forces could be, and no doubt was, in all four groups in the course of one year. But as the Act does not provide otherwise, I come to the conclusion that each exemption would only be applicable to the pay and allowances during the time the member was in that particular group.
There might have be some unfairness in the tax treatment of members of the military under the Income War Tax Act, in that exemptions were based on location rather than risk. What else is 'new' . . . or should that be 'old'? Another tax appeal highlights another possible unfairness.
In this case, a YMCA Supervisor, who accompanied the Canadian Army overseas (like hundreds [thousands?]) of others in the Sally Ann, Red Cross, YMCA, KofC, etc), wore uniform, was fully integrated in the unit that he supported, and was actually wounded, unsuccessfully tried to make the case that he should have been treated, for income tax purposes, the same as members of the military (all pay and allowances while overseas exempt), rather than the limited exemption of only one fifth of his income not being subject to tax.