I did some testing with a snippet of code provided by the manufacturer of the Ali chipset, but it lacked specificity: it detected any 386 processor not just their own.
IMHO, the best way to detect a Pocket/Book family of products is to query the processor type, the specific video display adapter, and the BIOS ID. But even after filtering all those specs, you may still get a few false positives.
Regarding other types of 386 processors, the most common Intel and its direct competitors (AMD, Cyrix, etc.) are well documented. The ones which are more difficult and error prone to detect are all the embedded third party variants which are mostly found on industrial SBC's and embedded special purpose devices.