"For maximum damage, activate abilities immediately after using light attack." This is a tip straight from ZOS, and it's how light attack weaving works in the game, you can hit a skill right after your light attack is in action.

But here's my problem with it which becomes clear while weaving light attacks between skills: different weapons have a different wait time from the moment you press the skill button to the moment you press the light attack button, which is made worse with a laggy internet connection.

*Update*
After a lot of testing on the latest PTS 5.2.4, and with the use of ESOlogs, I've finally been able to nail down the issue I'm having. I've been playing a Nightblade for years, and subconsciously set my rotation speed to ensure that every light attack lands to maximize the number of relentless focus procs. ESOlogs can tell me the rate I've been using skills during a rotation, and this weird update where Stam users can get a boost from the Maelstrom Staff has been very eye opening.

Here are my results of Builds tested on the PTS during prime time:

Nightblade Dual Wield front bar / Maelstrom Staff back bar
Method:
Use Elemental Blockade, then spam surprise attack / relentless focus 14 times per rotation on DW bar
Result:
54.3 Skill Casts per minute (100% light attacks landed)

Nightblade 2-H front bar / Maelstrom Staff back bar
Method:
Use Elemental Blockade, then spam Wrecking Blow / relentless focus 14 times per rotation on 2H bar
Result:
51.9 Skill Casts per minute (96% light attacks landed)

Nightblade Bow/Bow:
Method:
Use as many skills as possible that aren't snipe to keep the rotation fast-paced, hit relentless focus every 5 light attacks
Result:
46.2 Skill Casts per minute (97.2% light attacks landed)

Dragonknight Dual Wield / Dual Wield
Method:
Rush through a DOT rotation as quickly as possible, but try to get most light attacks to land
Result:
56.2 Skill Casts per minute (87% light attacks landed)

Dragonknight Dual Wield / Bow
Method:
Rush through a DOT rotation as quickly as possible, but try to get most light attacks to land
Result:
51 Skill Casts per minute (95% light attacks landed)

I got better DPS from the dual wield / dual wield DK build

So I'm getting 100% light attack weaving with 54 skills per minute, but only when dual wield is equipped. It drops drastically with a bow, and drops somewhat with 2-H. Other players apparently have no issue with bow, I've seen parses uploaded on ESOlogs where skills and bow light attacks land every 1.02 seconds. My bow attacks land every 1.25 seconds during prime time, 1.1 seconds at 3AM Wednesday morning, any faster and the light attacks mostly fail to land, I blame my spazzy internet, but still think it's a shame to see a whole weapon line effected.

You have to wait a split second longer to activate a bow light attack as opposed to dual wield or 2H or it never happens. This isn't entirely about the light attack spam speed, it's about pulling off complex rotations using the different weapons we have available.

Bow light attacks take the longest time to wind up after a skill activates, yet they have the shortest spam speed if the light attack button were pressed repeatedly. It seems like you have to wait 100 ms longer than with dual wield after activating a skill before you can que up a bow light attack. Or you could que a light attack 550 ms after the last light attack and it goes off immediately. I get that there's an animation taking place, the character needs to reload another arrow, but my character can apparently reload a bow like a pro sometimes and gets lazy at other times. Why is that???

The light attack weaving part of bow/bow gameplay can be annoying compared to the other weapons. Bow/bow requires a lot of perfect timing and less lag, which is another reason that Bow/bow will always underperform when I use it. Subconsiously I'm adding a fraction of a second to every skill I weave so the bow light attacks aren't skipped over in the rotation.

Mental lag and internet lag aren't nearly as punishing when weaving with Dual since those light attacks are much more responsive. With DW there is no problem when you que the next light attack shortly after the last skill goes into motion, then activate the next skill half a second after that. Both hits will que successfully, which results in no DPS loss. So I can rush sloppily through the DW part of a rotation and there's no downside. It offers the best DPS by default.