The research has compared a number of exercises to assess triceps brachii muscle activity. Here's what we know:
Do Either Multi-Joint or Single-Joint Exercises. Surprisingly, research has shown similar levels of triceps muscle electrical activity (EMG) when comparing multi-joint and single joint exercises. This is true with loads around 10RM for the traditional bench press, close-grip press, dips, and many variations of the triceps extension including lying, overhead, and pushdowns (Bohler et al. 2011, Soares et al. 2016).
Ditch The Exercise Ball. Pressing exercises performed on a Swiss/exercise ball or balance cushion are inferior to pressing on stable surfaces, and pretty much useless if you're actually strong (Saeterbakken et al. 2013). To maximally involve the triceps, employ a stable position with a stable load. In other words, you need a barbell and a bench.
Barbells Over Dumbbells. In many cases, the barbell and dumbbell variations of an exercise are pretty similar, but not when training the triceps. The dumbbell bench press and dumbbell overhead press don't stack up when compared to the barbell and Smith machine variations (Saeterbakken et al. 2011, 2013), probably because using dumbbells limits the absolute load lifted.
Go Heavy. You can't trick the triceps with light weights. It's well known that muscle activity increases along with increases in weight, but even when bench pressing with maximal acceleration and intent, heavier loads (up to 1RM) are better for triceps involvement than lighter loads (Newton et al. 1997).
Use Slight Decline or Flat Bench. The barbell bench press is the king of the triceps multi-joint exercises. You'll want to press on a flat bench or slight decline since triceps activation is superior at these angles compared to the incline variations (Barnett et al. 1995).
Bring Your Hands In. Compared to the wide-grip bench press at moderate loads, the EMG amplitude of the triceps is twice as high when using the narrow grip (Lehman et al. 2005).
How Should You Train the Triceps?
Heavy bench presses produce among the best EMG amplitudes for the triceps, in addition to respecting the anatomy and individual moment arms (the length between a joint axis and the line of force acting on that joint) of the heads of the triceps.
We can make the bench press even better at building the triceps by using a close-grip bench press, as this variation boosts the involvement of the triceps.
You might also perform the bench press in a way that stresses the top portion of the lift. For instance, perform a partial range variation like board presses (shown above) or floor presses. You should also train the bench press with variable resistance, e.g., using bands or chains.