Of course, although it is necessary to play the piano as instructed by the teacher, ettiquette dictates that you don't play at certain times. As a student I'm always wondering when to stop and start. Also when the teacher leaves the room to answer a phone, etc. shouldn't I stop and wait? Or could I play The Simpsons theme to occupy the time? The answer to the pencil conundrum is to tie it on a piece of string round your neck. Small talk with the teacher is often polite and social. But, as a student I also often find it used up a good 10 minutes or more of my lesson.

I'm annoyed by a student who makes a big deal out of looking at the clock. If I see this more than once during a lesson, I will reach for the clock (very small digital that is also a timer sitting on the top of the piano)and put it right before his or her eyes without saying a word.

Over time (pun not intended) I will get clues from the student about what he is thinking that clock watching has become important to him.

Since I have the timer handy, I might at a future lesson say play Hanon 1-6 from memory once through each, strung together, then tell me how long this took for you to play.
Not only is this "cruel and inhumane punishment" it has a lesson to it, I think.

Time that is being used goes quickly, time that is inactive is painful.

Also, a point of learning could be: "Stop when you have played for 60 seconds or, 30 seconds, or 10 seconds. There is value to being able to measure time accurately - and it can come from within, not from the clock.

Apply these short amounts of time to your lesson assignment, and you will be amazed at what can be accomplished.

While 30 minutes of practice might be the whole enchilada on the clock, the 10 seconds and 60 seconds or 3 minute practice gains are incredibly joyful if you realize you used then enjoyably and make progress.

Make a friend of the clock, not an enemy.

I tell students where to start, and I tell them when they need to stop. This is important because sometimes I ask them to stop something that is so smooth, it is no problem—to get to something else that is a problem.
The teacher should tell you. If the teacher doesn't tell you what to do, there should be no reason to fault your for filling the time. I use a cell phone, and I keep it turned off in lessons except in an emergency situation, but I work in a store. There are people to take messages for me. I only stop to use the bathroom, and I'm usually very fast. Before I leave the room, I tell students exactly what to practice.