A paper entitled "One hundred prisoners and a lightbulb" by Stanford mathematicians Paul-Olivier Dehaye, Daniel Ford, and Henry Segerman (whose delightful homepage deserves a discussion of its own and suggests he has spent some quality time with Gödel, Escher, Bach) appeared in the Mathematical Intelligencer. It is available as a preprint here, here, here, and here. In that article, a situation very similar to the two switch puzzle is described.

What is exciting about the paper is the degree to which it clobbers this problem! The authors provide several strategies for the problem, analyzing the expected time until the prisoners are freed for each. The first ends up with a nasty O(n^1/2eⁿ). This is dramatically improved by the second to O(n²). The third has an expected running time of O(n log(n)²), which is probably nearly optimal if not optimal. (In any case, the authors point out that no algorithm can do better than O(n log n).) They then proceed to consider a fascinating array of sixteen variations on the problem, including the formulation of the problem with random visitation times. Each of these is promptly solved. Finally, the authors give their "über-theorem": the prisoners can all reliably send each other messages of arbitrary length. Even more astonishing is the "über-über-theorem" that follows it: this can even occur in the scenario of random visitation times.

I highly recommend the paper. Thanks to Evan Danaher for pointing it out to me. Check out this page in the puzzle section for a little more info.