Viking mice

There aren't ruins or remains prior to the late-mediaeval Portuguese in the Azores or in Madeira. There are, however, mice. S. I. Gabriel, M. L. Mathias and J. B. Searle wrote about them in 2014.

The study marks the Madeira mice as Danes. Terceira in the Azores hosts Norwegian mice, "Clade F". Santa Maria also has Clade F mice but these're not (yet) assigned to Norway specifically. Clade F also inhabits the Gaeltacht and Iceland, which the Vikings also colonised - famously Dublin.

Danes and Flemings did assist the Portuguese and Spaniards in the Age Of Discovery, as "Dulmo" - Von Ulm - illustrated in 1487. However, it is not clear to these three authors how their mice should have so dominated Portuguese mice in the islands mentioned, as Portuguese mice dominate other Azores (which could well be Lishbûnati mice, whichever). It is even less clear to the authors how Scandinavian mice could have sailed over there without human help.

We do know of Viking raids into the Islamic side of Iberia. Most famed was that against Išbīliya (Seville) AD 844. The raiders had to row up the Guadalquivir for that. The Irish remembered that Dublin (a Viking city then) sent a raid still further 860ish, against Morocco. The Muslims didn't record whence the ships came but they did know they were "Majus" - "fire worshippers" - who hit Nekor.

More likely to the researchers (and to me) is that various crews of Viking disembarked at the islands mentioned, and not at the other Azores. From there they chose not to sing the sagas of the great rodent colonies they'd successfully installed, for whatever reason. Unless that's what the Irish overheard in Dublin...