Let's look at Jayce's playstyle, laning and teamfighting, and see why it isn't conducive to a trinity force.
Laning, you are primarily in cannon form. This is typically the point where you are trying to stack a tear, while farming every bit of armor penetration you can get for the mid game spike that comes with muramana. Already, trying to fit in a triforce, the most expensive item in the game, will be hard and likely cripple your power spike. Poke is primarily q and eq. Eq, you will not get a sheen proc off the majority of the time when you use it. Q trades really only need the q, as most of the time you are throwing it out and backing off from any retaliation, trying to whittle them down. Only all in kills in hammer form would benefit from sheen procs, as hammer q, auto, e is the standard hammer combo. And even then, the e disengages the attack, so follow ups will require chasing down in cannon form, something that we've already established has very little application with sheen procs the majority of the time.
Teamfights, Jayce is a siege pusher. He stays in the back line using eq to poke down the enemy while using regular q and w to push to turret. Any poke towards enemy champions will not use the sheen procs unless they are in range for your autos, which is too close for either your or their safety in a siege, as that's in range for almost all engage or cc in the game against you, and in range for hammer form q slow for the enemy. During actual fights, Jayce stays in the outside poking in with autos and spells. He will use most sheen procs at this time, but conventionally this should never happen if you sieged well, as any engage would have to be fast and before you poked them down. And even then, you can disengage with your cannon e, so it should further never happen. And even if they did engage after you poked them, you should already have the damage down necessary to win the fight through muramana procs.
In every way, trinity force on Jayce is just not a good buy. It delays your strongest powerspike for a weaker one, and it's inefficient to his playstyle. Armor penetration is more valuable on Jayce than the sheen procs and bruiser power on tf.