After doing a lot of thinking, dancing, trying out various footwork timings, and also asking my dance instructors and percussionist friends, I have come up with this new post. Let me know what you think! Again, these are just my thoughts (and the paraphrasing of comments made by others), but I think this makes good sense.
A Primer
Just as a primer, if you are not familiar with musical notation, have a quick read of this post. Also, please note that this post relates to linear/slot styles of dancing salsa - I don't think this timing applies to Casino/Cuban styles at all (Cuban timing is a lot more symmetrical/regular).
Notation of Dancing On1 vs On2
It the following diagram, the first staff represents salsa footwork when danced on one. The second staff represents footwork when danced on two. Note that the music is independent of this notation (e.g. the conga hits on all counts, the clave on some counts, etc).
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Dancing on the 1st Beat
When I was taught linear salsa (on one), the instructor pointed out that the timing is "quick quick slow". She didn't really know why, but it just worked. So, forward on one, back on two, then a slower step back again on three. One justification I worked out for this is that the next step was back on five, which was two beats away, not one... hence the slower third step. If you look at the first staff in the diagram above, you should clearly be able to map the "quick quick slow" of each bar. The important thing to note here is that the slow doesn't start on three... it starts on three and a half.
Dancing on the 2nd Beat
As for on two dancing, my instructor on the first day of class taught us using the term "slow quick quick". So, a slow step on one going back on the left, then quick quick for the break steps (back on the right, forward again on the left). This ties in with on one dancing... the quick quick is on the break step then the step straight after this. The slow is the transition step - the step that moves from one end of the slot to the other.
One slight catch with on-two dancing is that of starting the very first basic of the dance. Since it is a bit tricky to feel the "slow quick quick" on the first bar of the song (and that the "slow" beat, technically, starts half a beat before the first bar), it helps to count it as just "quick quick quick" or "one two three" for the first bar. From there, you can then go into the normal count of "slow quick quick". I have shown this "one two three" lead-in on the first bar of the on-2 staff. Incidentally, this is the same issue that percussionists face when starting a song with complex cowbell patterns (etc). So, they use the same trick... they will insert regular beats into the first bar of the song and then switch to the "real" syncopated pattern on the second bar.
The Subtleties of Timing
The "quick quick" steps are easy... for on one that is the "one two", and for one two, that is the "two three". However, the remaining step in the basic is a bit trickier. The "slow" step (both for on one and one two) is equidistant between each pair of quick-quick steps. Again, just look at the notation in the diagram above and you will see what I mean.
For on one, this means that your third step isn't really on the third beat, it is on 3 and a half (this extra half beat is just an equal share of the one extra beat between beat three and five). Same goes for the sixth and final step in an on-one basic... this isn't on the seven, it is on seven and a half (then followed by one two).
For on two, this means that your first step (the travelling step before beats two and three) is actually on eight and a half, not one (again, equidistant between each pair of "quick quick" steps, sharing the "extra time" of the slow step evenly). Same goes for the forward basic... the travelling step is really on four and a half, not five (then followed by six seven).
Please note (and this is important!): I am not actually recommending listening for the half beat and trying to step exactly then, but if you have the mentality of "quick quick slow" for on one or "slow quick quick" for on two, I think your feet will naturally hit this timing.
Other Observations
The second beat on each bar is interesting (have a look at the diagram again for this)... regardless of on one or on two, the second beat is always hit by footwork (despite being a downbeat), and there will always be a conga slap on this beat too (per bar). On a 2/3 clave, the clave will hit too.
I hope this helps clear things up a little bit. Personally, I have found this a really interesting topic to dig into, and I was surprised just how easily it was to figure out by using musical notation. I hope the diagram helps you too!