Heimdall is most famously known as Asgard's guardian. He also is associated with Rig, who taught the runes to mankind. In any case, teaching, runic knowledge, and intellectual pursuits are all within Heimdall's purview. He is very much a God of illumination in many different senses. While meditating, I have often found Him one of the very easiest Gods to "see," though I do not always have the easiest time with visual interactions.
Many of my personal encounters with Heimdall have been as a student approaching a teacher. This is not an uncommon way to relate to Him from what I understand. Like Forseti, He will ask questions and expect that real thought be put into the answers. He seems to enjoy honest emotion and honest discussions. He has a fierce passion for the Gods and Their realm that comes right from the heart. In this way He rather reminds me of Odin. Duty is hardly the only reason Heimdall stands guard: while one's role and one's deeds are important, He also reveals the ferocious drive, transcending value, and core of love underlying that which must be done.
Heimdall is an extremely intellectual God. With his connections to listening and understanding, as well as to teaching and illumination, I believe that He would be an excellent God to call on for any academic pursuit. Heimdall seems to have a very genuine warmth and regard for humanity--rather like Thor, but with a twist more towards various forms of development such as education or acquiring technological knowledge. This may seem to be a bit of a digression, but I was really hit with a sense of Heimdall's nature when I was--of all things--discussing the history of transistors with a friend. Transistors were the reason we were able to move away from vacuum tubes and ever-expanding, gargantuan computers to create the technology we have today. The manufacturing process itself is of interest, as it involves changing and layering crystals, often with a laser (or so I am given to understand, with only a lay-person's background in any of the sciences). This gets all the more amusing when some of the processes explicitly reference diffraction, the principle that also allows for the existence of rainbows. Then there is the way transistors work as switches, determining what gets through and what is blocked, and as amplifiers (remembering Heimdall's acute powers of hearing and sight).
Not surprisingly, Heimdall sometimes shows a keen interest in assisting with spiritual pursuits, including building up relationships with other Gods and Goddesses. I have found that He has excellent insights about spiritual practice, developing increased perception in meditations, and forging deeper connections with other Deities in our pantheon. One of the things I have learned from Him is that the bridge between worlds and our relationships with our Gods are not static: Bifrost itself is made of light, which is in constant motion. So too with our exchanges with the Divine. I admittedly have a great deal of trouble internalizing this concept, but connection really is more of a dance or a flow than a set-down path. Communication happens far more naturally if we can approach the Gods in this way.
Our Deities are much grander than our human preconceptions. We can sometimes perceive conflicts of interest where there may not be any, and avoid approaching certain Gods or Goddesses on that basis. Heimdall is a true friend of humankind and is an especially good God for any of us to hail or honor. Respect, as always, is key.
For more UPG about Heimdall, I recommend The Temple Of The Flea's Heimdall Pages. The site was created by a devotee of His and includes information on offerings.