What is the origin of the phrase "caught red-handed"?

Solution 1:

On etymonline you will find that it is, presumably, from the blood on hands.

There are other more detailed articles around, quote:

Red-handed doesn't have a mythical origin however - it is a straightforward allusion to having blood on one's hands after the execution of a murder or a poaching session. The term originates, not from Northern Ireland, but from a country not so far from there, socially and geographically, i.e. Scotland. An earlier form of 'red-handed', simply 'red hand', dates back to a usage in the Scottish Acts of Parliament of James I, 1432.

Red-hand appears in print many times in Scottish legal proceedings from the 15th century onward. For example, this piece from Sir George Mackenzie's A discourse upon the laws and customs of Scotland in matters criminal, 1674:

"If he be not taken red-hand the sheriff cannot proceed against him."

Solution 2:

George Macdonald Fraser, in his "Steel Bonnets", a history of the feuds and raids on the English-Scots border, says that pursuing raiders across the Border was not only allowed but in some circumstances compulsory, and

If... the robbers were overpowered, they were usually taken back as prisoners. On occasion they were cut down in cold blood or hanged on the spot; in the language of the Border, which has passed into the language, they had been taken 'red-hand', which was 'in the deed doinge'...

If this is right (and Fraser is one of the best sources on this subject), it's from the 16th century if not before.