Tom,
That's great to hear, I did not see that any where. I'm thinking simpler yet, just a bit more sophisticated than rotating the array by hand every hour or so. Slip rings are readily available too, make it non-reversing and go all the way around to home (or by time) during the night. Just a BA clock.
As Tom says, tracking by time isn't terribly difficult, but the process to actually work out where the sun will be with any precision is a computationally demanding task. I'm doing it on one of my systems for other purposes, and it does take a reasonable number of CPU cycles.
That said, I'm doing similarly to Tom - I have 4 arrays "tracking" (I use the term very loosely), by a very simple system of a gated clock. From sunup until sundown, the system drives the panels west 2-4 seconds every 20-30 minutes (exact times vary depending on time of year). A while after sundown it drives the panels to an overnight "park" position, and just before sunrise it drives them fully home.
With flat panels, an angle offset of 10 degrees from "ideal" represents only 1.5% loss of power, and for the sun to move from 10 degrees "east", past the panel to 10 degrees "west" takes roughly 90 mins to 2 hours (depending on time of day). So as long as you can move the panels to "close enough" to the right place, you're not really wasting a lot of potential.
Tracking the "beam" though is cool and makes for a neat demo, I guess that sells more.
Tracking the "beam" as you put it, is actually a fairly trivial task for a very basic electronic device to do. Certainly much easier than a clock of sufficient accuracy and features, and way easier than something able to compute the suns position at any given time. The mechanics may be more challenging!
As for ideal tracking, you should look up "polar mounts" or "polar tracking". Ideally, tracking in the polar plane, but with an additional offset for time of year should make the tracking process straightforward. The mechanics of such mounts often makes it easier to simply do 2-axis tracking electronically. 2-axis tracking also gives you the advantage of being able to (potentially) stow the panels in a reasonably safe position during storms.