The SSID broadcast for a wireless router has been disabled but a network administrator notices that unauthorized users are accessing the wireless network. The administor has determined that attackers

Upgrading encryption to WPA or WPA2 improves data confidentiality and authentication security but does nothing to hide the presence of the wireless network from passive scanning or probe request responses.

Creating a non-zero length SSID actually makes the network more visible, not less, as it ensures the SSID name is broadcast in beacon frames rather than being suppressed.

Rerouting users to a honeypot is a deception/detection technique used after unauthorized access is suspected, and does not obscure the presence of the wireless network from initial discovery.

Even with SSID broadcast disabled, wireless access points by default still respond to broadcast probe requests (null-SSID probes) sent by client devices scanning for networks, which allows attackers using tools like Kismet or airodump-ng to detect the network. Disabling responses to broadcast probe requests forces the AP to only respond to directed probe requests that include the exact SSID, making passive detection significantly harder. This adds a layer of obscurity beyond simply hiding the SSID beacon frames.