What is the origin of the idiom 'a beam in one's eye'?

I already understand and so ask not about this idiom's meaning. Though some idioms fail the Principle of Compositionality, this idiom seems to derive from imagery and so its semantic shift can be explained.

I am conjecturing that the 'beam' refers to a light beam, but is an outward beam biasing the hypocrite, or does the beam emanate from the hypocrite?

No, this is from Matthew 7:3-5, in the King James version

And why beholdest thou the mote that is in thy brother's eye, but considerest not the beam that is in thine own eye?

The word in koine is δοκός (dokos), meaning a wooden beam to contrast with κάρφος (karphos), a splinter or something light and dry. More modern translations use "speck of sawdust" for "mote" to make the contrast with two irritants that are made of the same material.

I am conjecturing that the 'beam' refers to a light beam ...

No, the idiom refers to a beam made of timber, and is used figuratively to compare it with a tiny speck (or mote). So there is no direction implied at all, either towards or away from the hypocrite.