Compound subjects joined by and are generally plural.

When subjects joined by and are considered a single unit or refer to the same person or thing, they take a singular verb form.

In this sentence, drinking and driving is considered a single activity, so a singular verb is used.

With subjects joined by or or nor, the verb agrees with the part closer to the verb.

If you find this sentence awkward, put the plural noun closer to the verb: Either the defendant or the witnesses are lying.