Perhaps an expert will come along and answer this for you, but in the meantime I had a quick look and got what appears to me to be a general consensus towards the Picts being of mainly Celtic origin. Cunliffe summarises the issue as follows:

"The Irish, Attocotti, and Picts were probably Celtic peoples, althought some linguists claim to be able to detect a pre-Indo-European element in the Pictish language." (263).

Of course, this quote demonstrates (at least in 1997) that nothing is 'known' on this matter, but we do have probability. A few more recent articles I have found seem to support the assertion that the Picts were of Celtic origin (Keys 41, Snow 46), but Teutonic influences later mixed in amongst the population of Scotland and became somewhat dominant, yet the modern 'Scottish' identity betrays a mix of linguistic influences including "Gaelic, English, Welsh, Norse, French, Flemish and Latin" (Hammond 6-8, 26-7). Celtic and non-Indo-European languages could also have co-existed:

"Though it is fashionable for scholars to ignore it, a non-Indo-European language does seem to be visible in the inscriptions of Pictland, which have never convincingly been interpreted as Celtic. The presence of such a language is supported by the ancient river names, so long as they are not emended. When Isaac analysed Ptolemy’s river names in Britain, he found between thirty-four and forty-one Celtic ones and six non-Indo-European ones, and five of those six rivers turned out to be in north-east Scotland. This is indeed what one might expect on the far edge of an island on the far edge of Europe" (Sims-Williams 431-2).

I've only collected some bits and pieces here and I'm a total layman on this matter so I may have horrible embarrased myself. But the summary of Cunliffe seems reasonable on the matter: that is, that the Picts were predominantly Celtic and perhaps had a smaller non-Indo-European aspect.

Sources:

Cunliffe, Barry, The Ancient Celts, London: Penguin Books, 1999 (1997).

Hammond, Matthew H., "Ethnicity and the Writing of Medieval Scottish History", The Scottish Historical Review, 85, 219, 2006, 1-27.

Keys, David, "Rethinking the Picts," Archaeology, 57, 5, 2004, 40-4.

Sims-Williams, Dean, "Bronze and Iron Age Celtic Speakers: What we don't know, what we can't know, and what could we know? Language, Genetics and Archaeology in the 21st Century", The Antiquaries Journal, 92, 2012, 427-49.

Snow, Dean R., "Scotland's Irish Origins", Archaeology, 54, 4, 2001, 46-51.