I'm finally after a long time of thinking about it, going to play a campaign of DnD. For that I have bought the starter set and I'm actually still in preparation for it. I'm going to be the DM and it is going to be a 1 on 1 campaign¹.

I found the 3rd approach of this answer:

http://rpg.stackexchange.com/a/59433/15211

is a way of doing it without too much effort while it still leaves the chance for 2 first timers (as we are) to concentrate on roleplaying just a single character.

I'm planning to play 1 character so my friend can play 1 as well. In addition I'm planning to just decrease the monster count so, that the XP treshold comes closest to the equal dificulty-class for just 2 players. For bosses I bought the monster manual, so I can look for a boss-like monster that still fits in the lore with equally fitting difficulty.

But there is one point left in my preparation that is hard for me to find a way to solve.

I know myself well enough to know: When I will be DM'ing a "story" that I already know, while I'm playing a character that is part of it, as long the character itself has a motivation to get ahead, I'll be playing it in an impatient pushing way, since I'm not good enough to winging the behavior of the character for every situation. I could make a plan when I have to respond in what way, but... all I learned so far, this won't help either, because things are going to come unexpectedly.

But I want to present the roleplaying aspect to my companion as well and I guess it will be a less intense experience, if there is no PC to interact with.

So I got so far:

I need to characterize a trait, behavior or background for the character that it has no ambitition to push the story on (so the PC can't become a tool of me to bring the story where I passively want it to get to and still leave the unfolding of the story in my companion's hands.)

But all ideas I had so far about a character that would satisfy this need, had one big flaw:

When I asked myself "And what is his motivation to even participate in this adventure?" There was no feasible answer to it.

So:

TL&DR

How to design a character in a way, that his trait, behavior or background when roleplayed correctly lets him not participate in decision-making², while it still is obvious that his motivations are a success of the "party"?

¹_{Among the cons of a starter pack, as I assume most know, is its difficult to play in this given set up.}

²_{Should the character be forced by another PC into making a decision, it is acceptable, since it is an exceptional case not caused by the GMPC's player himself.}