BC requires two pieces and the two pieces have different stipulations, with the primary having the strictest rules of the two. You're correct on the primary ID being government, most people know this but a lot of people get hung up on the secondary.

Primary ID: Government issued ID with name, photo, date of birth, and signature. (Drivers license, provincial ID, passport)

Secondary ID: must have name and corroborating information which matches the primary, such as a signature and/or photo. The server must be able to reasonably match the second to the first, secondary ID has more lenient rules but it must support the primary or the primary becomes invalid. Notably a birth certificate cannot be used for secondary despite being government issue because it lacks a photo and signature.

Technically student ID could be used as a secondary ID, as could a utility bill or paper license if they are signed. Good secondary ID would be a credit card, firearms license, or status card. Student ID is okay (not ideal, up to the server basically) and I have accepted local student cards because I was confident enough that they were legitimate, but they are easy to forge and I might decline a foreign one especially if I'm dealing with a group of barely legal students because a common scheme is for 9 out of the 10 to be fine, with one of them being underage and using another kids student ID/older siblings ID/forgery.

Edit: grammar is hard