you can for sure work remotely for an employer NOT in canada. so if i am a remote worker for company USA, and i have paystubs to prove company USA pays me on a regular basis, i can continue to do my job while in canada (using computer/internet/phone).
If I own my own business or am an independant contracter, then proving my employment in the US may be tougher. However, if i have contracts with and get paid by US companies (or any other company outside of canada), i can still do my job while in canada. Where it becomes an issue is when you are servicing canadian clients from within canada. while you may be able to do that from the us, it is a very gray area when you are in canada.
I've really never had to "prove" my US employment when asked this question by CBSA. if they press for more info and proof, then i usually show them my paystubs. my situation was quite different because i had an exclusion order at one point, so i always got sent to secondary after it was lifted. at first i always showed my paystubs, after a while, they just believed me because my answers were consistent with what i've said before. it's generally good practice to carry 2-3 weeks of recent paystubs and/or work contracts in case it comes up.
i did this for months without issue, and actually it helps you get through immigration quicker because when they see you are gainfully employed in your home country, they don't have a concern about you stealing a job from a canadian while you are there.
good luck!
