Pagers are not guaranteed to be 1 way comms and bringing them into secure locations is a security violation. Additionally, depending on the classification, no unauthorized and undisclosed devices of any kind would be permitted, including any electronics or electronic media such as tapes, CDs, discs, etc. Even when I was issued a verified 1-way pager, I was specifically briefed I was not permitted to bring it into a classified location. Most of the highly classified SCIFS are shielded anyways, you can’t use it inside so it’s safer to leave it out, along with all other devices.

If your organization allows it, then (if federal) they are breaking the law and should be reported/up-channeled. If it’s corpo, you should bring up additional concerns with your security team.