The RTL-SDR is an incredibly useful hack but started life as an HDTV receiver, there was little consideration to power savings beyond not maxing out a USB 2.0 port; I would guess they burn worse than 1A/H, they sure get hot aand that is before you add a band tuned LNA inline to receive weaker mobile signals(dispatch is probably pretty strong).
You can find the actual fire pagers cheaper and even the old ones with tiny crappy Ni-Cd batteries lasted several days in the 70s-80s, I guess the Minotaur pagers only got very small at gen6 before that they were cigarette pack sized up to a small brick for the 80s origonal. When I was just a volunteer though after getting permission and my callsign I clipped the wide TX enable wire(the old outside of amateur band mod) on my amateur handheld radio so I could call in accidents to dispatch or talk on tactical channel without taking a radio off of the engine/rescue/ambulance; now those little VHF/UHF Baofengs and the like are so cheap and easy to USB program with CHIRP I would do that even even just to listen to dispatch freq in an untrunked unencrypted system. That said I was already carrying the radio to use the amateur repeater for ham chatting as well as callbacks to non-ham friends on the telephone patch in the days(1990s) when I could only afford paging service not a phone. I recommend any volunteer fire/EMS people reading this especially new excited ones get clear permission and probably a real department radio callsign before they transmit or they can expect to get stomped on by the Chief maybe asked to turn in their gear and shown the door, or at least a stern meeting with the comm officer and their Lt/Capt.