How can I track lost iPhone after 24 hours without Apple ID access?

Is there no way to find the last location it pinged before (I’m assuming) it died?

No, if 7 days have passed since the phone last sent information about its location.

I’ve read elsewhere that last location is only stored for 24 hours.

Here is what Apple Support says.......

• If Find My can't display the current location (because the phone is powered off or otherwise not sending its location), Find My displays the last location sent by the device or the last known location on the Find My network.
• If more than seven days have passed since your device last sent its location to Apple through the Find My network, Find My can't display a location and instead shows "No location found."

It's not really possible to know if it is the battery that has run down or the battery is OK, but the phone simply cannot connect to the Internet where it is currently located.

iPhone thieves are very fond of placing the phone in a Faraday bag or simply wrapping the phone in aluminum foil to prevent the phone from either sending or receiving a signal.

Log in to https://icloud.com/find and see if it shows.