How are you adjusting reinforcement to reduce inappropriate initiations and to increase appropriate initiations?
What are some reinforcing consequences you can deliver either immediately following the desired behavior or following a practice session– things that this particular student enjoys, wants, seeks out, etc..?
Some students who rarely initiate might benefit from a point or tally sheet, where a certain number of points yields a special activity or reward. Keep in mind that this type of token economy may also need to take into account the quality of these initiations, and not just quantity. In your visual representation of this type of reinforcement system, the student needs to understand that “I did it!” and “I did it appropriately!” are two different things.
Are you using labeling and social praise to make the contingency between desired behavior and reinforcing consequence clear to the student?
What reinforcing consequences can you arrange that are more naturally or intrinsically connected to this targeted behavior?
Positive feedback from the conversational partner, and sustained interaction (in most cases), are the most natural motivators.