With auto-ranging on DMM's, sometimes when oil/dirt from my hands, gets on the probes, the DMM will take longer.
Can you really measure a time difference ? I'd use the same probes, even the same battery, turn on or off auto-ranging, and compare them.
As for books/manuals, look up DMM service manuals, most of the top DMM's from before the 1990/2000's, have nice detailed manuals, with theory of operation, and schematics.
There's lot of old analog volt/ohm/amp meters too, like Heathkit, all their manuals are in a few archives.
Heathkit Schematic and Manual Archive
https://www.vintage-radio.info/heathkit/Besides the chips getting smaller, I don't think much has changed, and most DMM's work about the same.
Fluke87 DMM
https://xdevs.com/doc/Fluke/83_85_87smeng0500.pdf