Although you do not want to use Twitter to directly market to your customer, you do want to draw them in so that you can market to them in other ways.
Your Twitter messages should be tailored to your follower in a way that provides information in an interesting way and leave them wanting more.
They should want to keep coming back for more and more.
The information you use to draw followers should: 1) An interesting tidbit of information such as developing news, hot topics, controversial issues (from a neutral perspective), business or industry facts, and most importantly free information they would otherwise not know or know where to find.
2) IMHO, every tweet should leave them wanting more.
There are three ways they can get more information: a) Return for more tweets.
Your follower will return for more tweets when consistent, good information is continually provided.
That does not mean you must tweet every hour but you must have a regular schedule.
I think you can tweet too much.
This can be annoying.
b) Follow someone else with similar information.
This is not necessarily a bad thing.
Hopefully, your information is compelling enough and interesting enough where it is unique and fills its own little niche.
If your information fills it own little niche, then even tweeters in the same industry won't be able to put a candle to you.
Tweet your message with passion.
In fact, you can use other tweeters to your advantage.
They now have it where you can retweet something someone else has already tweeted.
Follow people with information that is complimentary to your message but is not in direct competition.
Read their tweets and every now and again retweet the most compelling ones.
Don't overuse this method or it will backfire on you.
c) Draw them away to another website - It can be GREAT if you can get your follower to FOLLOW you to another website, preferably yours! How do you do this? Some of your tweets will be "discoveries" you have made of good information you have found.
In many cases, these discoveries can be new content you have posted on your website, blogs you may be writing, news relevant to your business.
The follower may not always be led directly to your website through a tweet can be led indirectly.
However, the follower should be led away to more of YOUR information.
Article marketing, blogs, tutorials, video marketing, podcasts, newsletters.
Any other content you have posted on the internet.
This increases your marketing exposure with this follower (and you are one step closer to converting this follower into a customer).
This new content you have led them to can lead them to other content you have posted.
Eventually, they will be led to your website.
Hopefully, your sales pitch on your website is strong enough to close the sale.
Don't use Twitter to try to "Close the Sale"; rather use it to "Open the Sale".
Attract more customers and traffic through Twitter.