Writing to offer a piece of information or a connection is a great way to demonstrate that you're looking out for the other person. Humans have a tendency to want to reciprocate, so the more you show you're looking out for someone, the more likely that person will begin to keep you in mind as well.
Don't consider sarcasm the 'be-all' and 'end-all' of verbal intercourse. Far too many people place way too much importance on the sarcasm instead of the talking, in and of itself, as a precious shared experience between people.
Most people try to escalate a relationship too quickly. Trust is built slowly, over time. Good relationships are built little by little, and there are no shortcuts, so do not try to push the relationship to progress faster than is natural. Because relationships are progressions, follow-ups are important.
Every day, do something selfless for someone else that takes under five minutes. The essence of this thing you do should be that it makes a big difference to the person receiving the gift. Usually these favors take the form of an introduction, reference, feedback, or broadcast on social media. Do something that's not for yourself, every single day. Expect nothing in return. Over time, these random acts of kindness will really add up.