Firstly, continue asking these kinds of questions about your magic. The answers to them will ultimately make you a better magician who is more well-rounded than those who are focused solely on technique. That said, I can assure you, with much confidence, that you are probably not yet perfect with your technique. I don't mean for this to discourage you, rather, to pose as an introduction to an argument of mine that I believe you'll find intriguing.
In weighing technique against presentation, I believe, they are equal as opposed to the idea that the presentation weighs more than the technique. If I were to change one card into another by means of a double turnover, and have controlled it with an overhand shuffle, all of the presentation in the world wouldn't hide bad technique. Although we'd still have an effect, it wouldn't be at its full potential. We must have passable technique to compliment my presentation. Now, the same thing goes should I have flawless technique with a presentation that is less than. In the latter I still have the effect of a color change, but the effect isn't as strong because my presentation didn't set up the effect as effectively as it could have. With this idea of balance in mind, I pose to you that decent technique, technique that is efficiently done, combined with a strong presentation creates strong magic. Yet, and I know this seems trivial, perfect technique, technique with the "Vernon Touch," combined with strong presentation creates stronger magic. Dare I say miracles? All of that is to say, don't stop working on your technique. Your magic will still improve as your technique does.
Having just stated that presentation is suppose to compliment the technique, and vise versa, I will note that I'm referring to the "sub-genres" of presentation. For example: the specific placement of props to facilitate in-transit actions, or using eye-contact to change the framework during a particular sleight. However, your question singles out the sub-genre of "Connection." Unless our audience is made up of magicians, they will never connect with our magic. We connect with our magic, and we also connect with our audience. In other words, we connect with our audience and then, through us, our audience is connected with our magic. If the audience wanted a direct connection with magic they would become magicians themselves. That is not to say that they don't appreciate good magic, they do, but magic is something to share with our audience, not to give to our audience. For us to make this distinction we must first personably connect, through our character, with our audience.
Our character is someone who we have to live with in a way since it is a representation of us. Though it may exaggerate certain aspects about ourselves, I believe that the main point is that we remain relatively true to our natural self. This, at the least, makes the transition into our magic easier. Personally, magic is a lifestyle for me. Therefore, my character is as close to my natural self as possible! In turn, it's extremely easy for me to turn a conversation into a short close-up routine. But first, I need to connect myself with the audience. This kind of connection in close-up magic is merely building the social skills, and then leading them into an interest in magic. So how do we build interest? One word - Patter.
If we use "Patter" without magic, we are telling a story. No, there is no trick happening in the moment, but we can use the story we tell to gain interest and help build a stronger rapport with our audience. Try using patter before performing any magic. Use it to have the audience to start investing in you and your character. Once they start to care about you they will also, in turn, care for your magic. Write out these stories and then practice leading into a magic trick from the story. Now, here's where everything gets ties together . . . Your character comes from you, your stories come from your character, and you magic comes from your stories and the narratives that you tell.
In short, develop your natural self, and you will naturally develop your character. In developing your character, you will find stories that connect with your audience and build interest in your character. These stories can then act as an outline to your magic by giving it somewhat of a structure/ context. All of which aid in your presentation. To be honest, this is not the only formula for improving your presentation, but it most certainly is a good place to start.
P.S. After re-reading what I've just written I hesitate to post this since I'm not certain if I've answered your question, let alone made any sense. So please forgive anything that doesn't make sense and know that I sincerely hope you can take something useful away from this writing that borders on the sanity of sleep deprivation. Respectful apologies,
Cameron J. Braxton