Let the player play two characters
I know this might not be exactly what you're looking for, but maybe you just let the other person play two characters instead of having one of your own involved. This can be a bit tricky with him trying to play two characters, but in a recent campaign I played in (1 on 1). I played a barbarian and a wizard.
The only thing is that I had to describe how the characters interact and speak with one another. In my case, the female barbarian was kindof a practical slob and the male wizard was prissy and clean. I might suggest the player making two characters who are very different so the interactions are more interesting.
As the DM, you then just have to throw the encounters at them and worry about your NPCs that you're using to interact with them. The problem with a GMPC is that even if you're trying really hard, you know exactly what will happen. So the solution is to let the player make all the decisions anyway...why not just let them play two characters?
In combat control and sounding board only
You may also decide that your GMPC is only under your control in combat and as a sounding board for the PC. The goal of the GMPC would tend to er on the side of caution in almost every circumstance (you NEED to be consistent in how he behaves otherwise you risk hinting things to the PC).
Your GMPC is a slave/servant
In 3.5 there was a character called a Red Wizard of Thay, and they had sword guardians called Thayan Knights. The Knight was completely subservient to the Red Wizard and absolutely devoted to his protection. You might also imagine Chewbacca from Star Wars, where he owes a Wookie life debt to Han. They have individuality, but ultimately, they follow the lead. A martial character would probably be appropriate for this sort of thing.
Tonto or Mute
I was thinking of characters that could emulate what you're looking for, and you're really looking for a sidekick. Tonto, the Lone Ranger's sidekick generally just had words of wisdom and had specialized environmental knowledge (the desert). You could execute a similar character where he has just a few generally wise things to say, but is really there as some comic relief. It might be an interesting opportunity to create some cryptic words of wisdom that the other player will have to decipher.
I also thought of a character who might be mute for some reason (imagine perhaps a witch cursed him because he kept running his mouth). That way he won't be able to give specific advice in any given situation, but rather would indicate 'yes', 'no', or 'I don't know' to questions from the player.