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.
Edit: Also, it goes without saying, current events are probably a good reason why pagers (and other devices) aren’t allowed in classified areas. While most focus on disclosure (getting out), we must not forget the risk of data/operations getting destroyed.
There’s also no such thing as “Military Grade” Encryption. The government as a whole, as directed by NSA, uses the same encryption technology. If anything, one of the defining techniques is how said technology is implemented as a process. That means less about the algorithm and more about the hardware and handling. For example, when dealing with classified networking, one of the key differences is using dedicated hardware. These aren’t PC’s that can be hacked, they are devices whose specific role is to handle encryption, key loading, or key acquisition. They are hardened to prevent emissions from leaking and will dump keys, firmware, memory if tampered with. End devices can only accept keys with no way to retrieve them for reuse.
Advertisers that claim they are offering you “Military Grade” encryption just do regular NSA encryption methods in software, with no hardware component, and no handling process. Which would never be used in the military to secure classified data.
Also, most encryption used in these devices don’t use one key, they use key generators. Each device talking to another generates a unique, temporary session key. These session keys do not last long, so if any one key is compromised it limits any potential unauthorized disclosures. Capturing encrypted data for later cracking would prove to be a time and resource exhausted process that would provide too little information, too late. At this point it would be easier to actually try to steal the keys and hardware, rather than crack them.