いそいそ

Etymology
Cognate with.

First attested in a text from 1212.

Adverb

 * 1)  cheerfully, eagerly, with alacrity

Usage notes
May optionally take the adverbial particle.

Verb

 * 1) to be cheerful, eager, and acting with alacrity

Usage notes
Not all sources treat this as a verb,  likely because all such adverbs can be used with the light verb.