Most evidence or interpretation indeed rely a lot on our understanding of oghamic script, but as well on onomastic (study of personal and location names) in ancient and early medieval Scotland.

(I'll mention the recent proposal that Pictish imagery reveals linguistic elements for the sake of it, but let's say it's far from popular currently to say the least).

I don't think someone seriously tried to pull a Pictish grammar giving the meager linguistic evidences at disposal.
A good in-depth reading on regional onomastic might be Approaching the Pictish language: historiography, early evidence and the question of Pritenic by Gudo Rhys

So far, there's two broad consensus on Pictish.

First, that Pictish is a Pritenic (northern Brittonic) language, and that the oddities and apparent gibberish in oghamic scripts are just pointing to misunderstanding them. This develloped from a reaction against the hypothesis of Pictish as a pre-IE language which was dominant in the second half of the XXth century.

A good introduction there would be Language of Pictland, by Katherine Forsyth.

A second consensus argues in the survival of non-Celtic and/or non-IE language along side a Brittonic language in Northern Britain. This stresses the plurality of northern Britain against a homogenic perspective of an ancient Pictland. It is true that Picts, like virtually any Barbarian coalition in Late Antiquity, emerged not from an unified cultural background, but first as a coalition led to resist and/or raid Romans,and that a rough political unity doesn't equal a cultural unity (medieval Picts being themselves importantly "Scottisized")

There's fewer extensive sources, for the time being, but it's a stance defended by Graham Isaac, Jonathan Jarrets in particular and among others.

And of course, between these two poles, there is room for other variants (for instance Gudo Rhys seems to defend the thesis of an overwelmingly Pritenic Pictish with possible survival of pre-IE elements).

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