It is neither.
I find it useful to think of English verbs as falling into three classes.
The vast majority of English verbs have only a lexical role and no grammatical role. For example, "see" has meaning all by itself, but it is not conjoined with other verbs to alter the tense or voice of another verb. Let's call a verb that can play only a lexical role an "ordinary verb."
A small number of verbs such as "will/would" and "may/might," have only a grammatical role and no lexical role. When conjoined with another verb explicitly or implicitly, they alter somewhat the meaning of the other verb. However, used without reference to another verb, they have no independent meaning. Let's call a verb that can play only a grammatical role a "modal verb."
Exactly two English verbs, "be" and "have," may be ordinary or modal. Each may be used as having meaning all by itself. Or either can be used in conjunction with a verb to alter the tense or voice of that conjoined verb, which carries the main meaning.
The terms "helping verb" and "auxiliary verb" mean the modals plus "be" and "have" if the latter are being used in their grammatical role. That is, sometimes "be" and "have" are helping verbs, and sometimes they are ordinary verbs.
I have a book
is a sentence where "have" is being used as an ordinary verb.
"Linking verbs" are a kind of ordinary verb. When "be" is used as an ordinary verb, it is always a "linking verb." When "have" is used as an ordinary verb, it is never a "linking verb."