While the verbs "behave" and "conduct" are similar in meaning, they behave slightly differently syntactically (phew!).
For starters, we should carve off the meaning of "behave" that implies "well." As other responders have pointed out, using "behave" without a reflexive pronoun, adverb, or adverbial phrase includes the meaning of "nicely" or "so as not to offend people." It is used most commonly in regards to children's behavior. We can also suggest this meaning with a reflexive object while omitting an adverb (e.g. "Behave yourself!") In fact, I have a hunch (perhaps someone can work with me to confirm it) that the now-common imperative "Behave" is just a shortened form of "Behave yourself!" Shortened because you can't behave anyone else, so why include the reflexive object?
"Conduct" is never used in the same way as this form of "behave."
With its behavior-related meaning (as opposed to its meaning of planning and doing (e.g. conduct research), of guiding a performance (e.g. conduct the choir), of guiding someone (e.g. conducted the tour group to...), or of acting as a conveyance medium (e.g. conduct electricity)), "conduct" has an obligatory reflexive object (e.g. herself) and an adverbial phrase (e.g. in a manner befitting a duchess).
Outside of the meaning / usage of "behave" outlined above, but with the same meaning of "acting in a certain way," "behave" has an obligatory adverb (e.g. nicely). In this way, it is similar to the class of words including certain meanings of "augur," "bode," "mean," and "treat."
Source: English Verb Classes and Alternations, Beth Levin