Igniting Oil Slick for TA/-

Well if you aren't giving a specific order you're generally relying on the ones with a Fire AoE catching it by chance and unless you get lucky with a cone attack that probably means the Ember Demon's fireball. You're probably best off either attacking it yourself or manually ordering a minion to attack it (the Fiery or Hellfire Demonlings would seem a sensible choice). You might even consider making a bind/macro to specifically target the slick and order a minion to attack it.

Dark is actually a better choice as a secondary to go with TA.

To answer the OPs original question you can pretty much do what you want with the secondary (don't forget that defenders get /fire now) you can put the posi proc in your AoE powers and if it procs it will ignite the slick. You can also use any temp power that does fire or energy damage (the rune of warding from Croatoa fits this bill as it does energy damage and can be infinitely renewed by flashing back the story arc that it is rewarded in)

This is probably the easiest way, as it requires no restrictions in choice of secondary.

If you are worried about redraw, your best choice is Archery.

If you aren't too worried about redraw, you can play tactically using a TA/Beam Rifle for some pretty interesting possibilities. The AoE from Oil Slick complements the relatively low AoE damage from Beam Rifle and can be lit by every single attack in Beam Rifle. EMP Arrow combined with your Beam attacks will apply a very strong -Regen debuff, making AVs much easier for your team to take down. I've been contemplating making one myself, but I'm reserving my time for a Titan Weapons character once that set is out.

Care to justify this?

As I said, Archary has lots of AOEs. I think you only really care about rain of arrows and doing it after an oil slick though.

Dark? -Tohit? Who cares in today's game of softcapped defenses? I certainly don't. You are left with somewhat weaksauce AOEs that don't really complement the ranged AOE focus of Trick Arrow in my opinion.

Archery has the singular bonus of no redraw as well.

I wouldn't even consider dark as a top contender. Assault Rifle and Dual Pistols are okay because at least their nukes are up often, but they are obviously more problematical with cones and PBAOEs than archery is.

Fire of course is going to be fine with its AOE focus. Maybe even Rad and Ice. And of course sonic is always good with the defender -res mods. But dark? I utterly fail to see any synergy at all.

It has 3, one of which is has a 50% knockback on each target which in my opinion is far worse than no knockback or 100% knockback. When I've used explosive arrow I found that it worked at cross-purposes to my other area attacks and location-based debuffs.

There are of course times when you can try to knock things into the location debuffs, but that ugly 50% chance pops up again so even this use isn't terribly reliable.

The fact that soft-capping is possible doesn't mean that every character of every player has achieved those levels of defense, or even will. And it's even less likely they'll have that against every single position and damage type.

They don't pump out large individual orange numbers, but they certainly do a boatload of little ones that melt large groups. And they do it every 10 seconds (before recharge) as opposed to every 60.

FYI the "weaksauce" AOE DPS of dark blast's two cone powers is almost as much (94%) as that of archery using its 3 area powers (ignoring the knockback issues for the sake of numbers), and surpasses archery (107%) if torrent is also used (again, ignoring knockback issues).

The damage proc potential is also greater with dark, if that's your thing.

The real handicap to damage is not having Aim in the set. That's never stopped me from doing sustained, consistent damage and cutting through large mobs of enemies.

Stacking -tohit with attacks and flash arrow.
A reliable area knockback power for when needed (like pushing people into location-based debuffs).
A cone immobilize that keeps enemies in debuff fields, but does not suppress knockdown; if that's not synergy with oil slick, I don't know what is.
An area stun for another control type to add to TA's controllery feel.

These may not be synergies that fit with everyone's play style, but they are definitely there.

This. Works great all the way up to 50 and beyond. You can even make a targeting macro so you don't have trouble finding the slick in a crowded battlefield. Slick, Target, Apprentice Charm. Works like, well, a charm.