According to the AT command reference v1.7, the nRF9160 SIP modem firmware v1.3.1 added the %PERIODICSEARCHCONF command.
It does though not mention anything about the behavior of modem firmware v1.3.0 and earlier.
From my (limited) observations with modem firmware v1.2.0 hardware SICA B0A there is a 10sec search interval and after some timeout a 12min sleep.
Do you have detailed information about the search behavior? I'm especially interested in modem firmware v1.2.0 and v1.3.0.
Reason for my question: I'm using a multi-profile SIM card which rotates its profile to a new IMSI every 3min (while registration fails). This needs to be synchronized with the sleep pattern, because currently with modem firmware v1.2.0 the modem enters those 12min sleep intervals while the rotation of the SIM profile continues. Those SIM profiles active during the modem sleep are not used for attaching attempts.