(I’ll be updating this with specific book recommendations… soon)
Field Linguistics Manuals
Especially the Morphosyntax related ones. Many field linguistics focus a lot on how to get information out of the head of the fluent speaker. Those techniques, obviously, don’t work as well for conlangs.
If Language is Community
You will want to read up on Endangered Languages. All conlangs are stillborn and have to be (re)vived to become living languages. The “vivication” process for a conlang is the same as the revival process for an extinct language. (And clearly not the same as the process for reviving a language that still has child learners, but sort of similar to the situation of languages that have lost all their child learners because, like conlang fans, all the new learners are learning the language as an adult and lack a pre-existing community.
You will want to read up on Bilingual Culture. Without a feel for when and how to switch among languages, a conlang will not be able to compete with the primary language. If the only social script your conlang fans have is the “speak one language at a time” script, what room does that leave for a conlang?
You will want to read up on Language Acquisition. The community-oriented conlanger is a teacher, or isn’t really an effective community-oriented conlanger.
If Language is Just Noise
Read as much as you can about phonetics and diachronic processes.
Popular Linguistics Books
Odds are, if you are a conlanger, you aren’t a professional conlanger or professional linguist. A good conlanger has a very broad, but superficial understanding of a variety of languages and language mechanisms. Unless you just want to create Romlangs. In that case, of course, specialization pays, but even then, the more interesting variations on Latin will be inspired by features of exotic languages or the (potentially misunderstood) theories of this or that.
How could I forget! Arika Okrent’s Book Land of the Invented Languages.
And that book about Hildegard’s Unknown Language. Haven’t read it but it has at least 1 chapter on conlangs in general.