L-PERIPH, second position, question clitics, and complex clauses

We’ve been using the L-PERIPH feature for e.g. second position clitics and generally to mean that something is in the left periphery of a clause. However how would this work with clause-embedding verbs:

(1) Ty  znaesh,  videl    li Ivan     Mashu?
    2SG know.2SG see.PAST Q  Ivan.NOM Masha.ACC
"Do you know whether Ivan saw Masha?"

If binary phrases say that their second daughter is [ L-PERIPH - ] then, under the head-complement rule, a verb cannot take a clause with a second position clitic as its complement.

Does it perhaps indicate that the clitic is not in fact second position (is “second position” strictly with respect to the whole string-sentence rather than a clause?)