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So, I've often had a hard time finding the Khajiit merchants, and the wiki articles (that I've read) are rather lacking. So I'm doing a bit of my own research and posting the results here, and later probably/maybe copying them over into the wiki.

First entry: after a few days staking out Ri'saad's camp by Riften (they never have tents when they're there -- what's going on there?), I spotted them heading out towards Whiterun, so I decided to follow them. Here's the log:

3:30PM leaves Markarth
6:30PM between Reachwater Rock & Sky Haven Temple
on south side of river (which probably has a name)
7:30PM pass near Reachcliff Cave
on south side of river
9:15PM between Old Hrolden and Valthume, near not-on-map shrine to Dibella
9:40PM cross bridge river
10:45PM pass near/north of Gloomreach
1:00AM pass south of Fort Sungard
2:30AM pass between Sunderstone Gorge and Broken Fang Cave
4:00AM pass near/north of Bloated Man's Grotto
4:45AM pass near North Brittleshin Pass
6:45AM pass near/southeast of Fort Greymoor
7:45AM pass near/north of Western Watchtower
9:00AM arrive at Whiterun campsite

I have a suspicion that their pace is a bit slower when I'm following them, since I suspect my presence increases the number of world interactions.

I've also noticed that if I stand around and wait (using the "wait" operation) for the Khajiits to depart, I can get them to stay for at least 3 days (that's when I get tired of waiting). It doesn't seem to help if I duck behind a building or something so they're out of sight. In the two cases I tried, 3 days of waiting in 4-hour intervals wouldn't get them to leave, but fast traveling away to the nearby walled city and back again got them moving.

So, in the same way a "watched pot never boils", a watched Khajiit never leaves.

Next journey: following Ma'dran from Windhelm to Solitude:

10:00AM - depart Windhelm
11:40AM - betwen Anga's mill and Morvunskar, cross River Yorgrim S->N
12:15PM - pass Anga's mill
1:40PM - pass by Yorgrim dragon mound
30-min distraction by Taron Dreth
3:00PM - pass by fork in road for Winterhold
3:20PM - pass South of Forsaken Cave
4:45PM - pass north of Nightgate Inn
5:40PM - pass south of Silverdrift Lair
7:15PM - pass north of Weynon Stones
20-minute distraction by Thalmor & dead prisoner encounter
8:15PM - pass west of Duskglow Crevice
9:00PM - pass west of Fort Fellhammer
10:30PM - pass east of Red Road Pass
11:45PM - pass south of Windward Ruins
12:45PM - pass north of Mzinchaleft
3:30AM - pass north of High Gate Ruins
? - lose track of them when they swim across mouth of the Karth River
7:30AM - pass under Blue Palace bridge, heading south, on west side of Karth River
8:15AM - pass over East Empire Company Warehouse entrance
9:30AM - arrive at Solitude campsite

I’m “greatly” interested in this subject. I have map images I believe from a Reddit user that mark their paths. I believe there is a bug that causes their arrival and their tent setups to become out of sync, but no one can explain why or how. Occasionally I’ve gotten the party out of sync with each other. (One lone Khajiti at the tents, etc.) I’ve questioned if the fast travel methods corrupt their timing somehow. I’ve also had your suspicion of them being slower when I follow. I went so far as to try and walk ahead and dispatch known attack spots but I would always seem to fail somewhere or give up.

So, I have collected quite a bit of data using "WAIT" and then using the PC console commands to teleport to where the caravan spawns. In almost every scenario there is some type of random world event or spawn point; animal attacks, spawned in travelers, thieves, hunters, etc. I have not exhausted every combination start location and wait time, but it does not appear as though "every" spawn point along the path is used. I also have yet to detect a clear correlation to the distances traveled and specific waiting times used. In every tested case between Whiterun and Markarth the specific wait time would cause them to move to the same location. I began collecting this data to report consistent results. However, the journey from Riften to Dawnstar appeared to contain at least two different patterns, yet I could not determine why one or the other was chosen. I also discovered on PC the Caravans initially spawn at the camps in Solitude and Riften and beginning the journey to Whiterun starting near Markarth. But on PS4 and the initial release on PS3 the caravan is not yet at Riften. Without console commands I attempted to find them on route, but have yet to find them with this method. Once I followed (wait 1 hr and teleport to caravan's next location) all the way from Dawnstar to Riften, only for them to begin heading back to Dawnstar only minutes after arriving at camp.
Have you ever used to the Clairvoyance spell to show you the path to your next target location. Sometimes it goes buggy and would have you going in very strange directions. (Some claim it is because you have selected multiple targets and the spell gets confused. While this is true; I have had the spell give me buggy directions for simply any random reason at all.) My point is that I think the caravans use a similar path finding mechanism....and sometimes it goes wonky or if they have traveled too far from the standard path, they may intentionally take an alternate route.
There is a chance I may not come back to this for a while. The random variations in the caravans are starting to spark a bit of insanity. (lot's of wasted time for little result) I did want to leave with this final note. There is a bug with merchants that lock you out of their stores at incorrect times. I learned that if you leave while their dialogue continues and they follow you out; this appears to be the primary cause for the bug. The merchants have specific timed action packages and it appears the order gets broken. But by waiting specific intervals; and allowing their packages to run in order, you can correct this timing. Something like standing outside and WAIT till time for them to wake up. Then WAIT for them to leave to eat at the inn. Then WAIT for them to go to bed. Then WAIT for store to open the next morning. This apparently allows for all the actions and "clear actions" to take place in the code.
I mention this because I believe this is what causes most of the bugs with the caravans (not counting mod issues). I believe it is a package timing issue. In my current play through I was able to fix a caravan that had a timing problem by arriving at a camp location and using a combination of entering the city doors and waiting for intervals for them to arrive; set up camp; stay for a couple days; and then travel to the next camp. Although this worked, I do not yet have a consistent step guide for the fix nor a consistent way to cause the bug in the first place. This is very similar to how PC players have fixed their broken caravan timing using console commands. I would just like for the rest of us to have that option.