Since your triceps are made up of about 67% type II fibers (fast twitch), they grow better with heavier weights and lower reps. Lighter sets using a lot of reps just don't do much for tri's.
With that in mind, I like something I call "infinity singles" for triceps, which is a riff on rest-pause training. You start with heavy sets of around 5 reps, then work your way down to doing singles as you fatigue. You keep the single reps going until failure, which surprisingly takes a while.
Here's how it would look with single-arm rope pushdowns. Trainer Aaron White demonstrates here, but we abbreviated the set for demo purposes. In an actual workout, one set can take a couple of minutes.
Start with a weight on the stack that you can lift about 5 times. You'll use the same weight throughout.
Using one arm, do 5 reps. Now immediately switch the other arm and do 5 reps. Squeeze the triceps hard and hold the contraction at the bottom for a second or two. If you're not making an ugly face, you're sandbagging it.
Without rest, go back to the first arm and do as many reps as you can. It might be 4 this time since your "rest period" only lasted as long as it took to do the other arm.
Continue going back and forth between arms, without rest, until you can only do 1 rep with each arm.
Here's where the infinity singles begin. What you'll notice is that you can keep doing single reps for a LONG time. That's because each arm is getting around 10 seconds of rest between each single. That's just enough time to recover and be able to do another rep.
Stop this extended set when you just can't do another single in good form. Your triceps will feel so pumped that they almost cramp up.