On which musical properties do tonic and agogic accents demand emphasis, respectively?

Respectively, the emphasis goes on pitch and duration.

Explanation:

Tonic accents emphases on pitch. By definition, a tonic accent in classical music is the attention given on a note with a particularly high pitch. Tonic accents in general refer to the pitch that a sound has.

Agogic accents emphases on duration. A variation on the duration of a note will make the beat stronger, where otherwise it would sound flat and without an accent.