@cicerone imposter,
$4 - $5 per day/per passenger is the standard for tour directors on American-based tours
the tour director has so many responsibilities, before and during the tour, including being on call 24 hours a day in case of emergency
best to do this yourselves, not as part of a larger group of tippers as that seems to drive the total to the tour director down
some companies put suggested tipping amounts right in the tour package - some indicate if it's permitted/not allowed
while most books/sites recommend the tip at the end, it's another place where my dad has often provided a portion, 25 - 30% of the total, upfront. i.e. on a 10 day trip, the total for 2 would be $80 - $100 to the tour director. $25 (from a couple) at the end of the first day in anticipation of all the work they'll have to do is a good move. that way, if there's rescheduling required, or whatever, your odds of getting an upgrade when possible are improved